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Journal articles on the topic 'Codes orthogonaux'

Author: Grafiati

Published: 25 May 2024

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1

Yen, Chih-Ta, Ing-Jr Ding, and Cheng-Mu Tsai. "PERFORMANCE ANALYSIS OF SEVERAL QUASI-ORTHOGONAL CODES OPTICAL CDMA FOR RADIO-OVER-FIBER SYSTEM." Transactions of the Canadian Society for Mechanical Engineering 37, no. 3 (September 2013): 415–26. http://dx.doi.org/10.1139/tcsme-2013-0031.

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An optical code-division multiple-access (OCDMA) network for radio-over-fiber (RoF) transmissions was proposed. The network encoders/decoders (codecs) were structured based on arrayed-waveguide-grating (AWG) routers coded using modified prime codes (MPCs). In the proposed system, the lower in-phase cross correlation could reduce the beating noise, and in the proposed study, its performance was compared with that of a conventional system that uses M-sequence and Walsh-Hadamard codes. The performance of both systems was numerically evaluated by analyzing the effect of phase-induced-intensity noise (PIIN). The results showed that the new code families that had lower cross correlation can suppress the intensity of the noise and effectively cancel out the multiple-access interference (MAI) in balanced detection processes, which improved system performance. By using the proposed MPC-coded OCDMA ROF network codecs, each network required only two AWG routers to accomplish the spectral coding of radio base stations (RBSs) and the decoding of control stations (CSs), resulting in a simple and low-cost system. Therefore, it is possible to produce interference- and crosstalk-free optical CDMA systems for RoF transmissions.

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2

Mienkina, Martin P., Claus-Stefan Friedrich, Nils C. Gerhardt, Martin F. Beckmann, Martin F. Schiffner, Martin R. Hofmann, and Georg Schmitz. "Multispectral photoacoustic coded excitation imaging using unipolar orthogonal Golay codes." Optics Express 18, no. 9 (April 15, 2010): 9076. http://dx.doi.org/10.1364/oe.18.009076.

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3

Tong, Ling, Qiong He, Alejandra Ortega, Alessandro Ramalli, Piero Tortoli, Jianwen Luo, and Jan D’hooge. "Coded Excitation for Crosstalk Suppression in Multi-line Transmit Beamforming: Simulation Study and Experimental Validation." Applied Sciences 9, no. 3 (January 31, 2019): 486. http://dx.doi.org/10.3390/app9030486.

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(1) Background: Multi-line transmit (MLT) beamforming has been proposed for fast cardiac ultrasound imaging. While crosstalk between MLT beams could induce artifacts, a Tukey (α = 0.5)-Tukey (α = 0.5) transmit-receive (TT-) apodization can largely—but not completely—suppress this crosstalk. Coded excitation has been proposed for crosstalk suppression, but only for synthetic aperture imaging and multi-focal imaging on linear/convex arrays. The aim of this study was to investigate its (added) value to suppress crosstalk among simultaneously transmitted multi-directional focused beams on a phased array; (2) Methods: One set of two orthogonal Golay codes, as well as one set of two orthogonal chirps, were applied on a two, four, and 6MTL imaging schemes individually. These coded schemes were investigated without and with TT-apodization by both simulation and experiments; and (3) Results: For a 2MLT scheme, without apodization the crosstalk was removed completely using Golay codes, whereas it was only slightly suppressed by chirps. For coded 4MLT and 6MLT schemes, without apodization crosstalk appeared as that of non-apodized 2MLT and 3MLT schemes. TT-apodization was required to suppress the remaining crosstalk. Furthermore, the coded MLT schemes showed better SNR and penetration compared to that of the non-coded ones. (4) Conclusions: The added value of orthogonal coded excitation on MLT crosstalk suppression remains limited, although it could maintain a better SNR.

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4

Wirastuti, N. M. A. E. D., I. M. A. Suyadnya, and D. C. Khrisne. "Performance Assessment of OFDM System using Reed-Solomon Codes over Fading Channels." Journal of Electrical, Electronics and Informatics 2, no. 2 (August 31, 2018): 48. http://dx.doi.org/10.24843/jeei.2018.v02.i02.p06.

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This paper study the performance of Orthogonal Frequency Division Multiplexing (OFDM) system over AWGN and Rayleigh fading channels. OFDM performs multi-carrier transmission where all the subcarriers are orthogonal to each other. The channel coding was applied to improve the OFDM system performance. Reed Solomon (RS) codes was chosen that an efficient channel coding algorithm and has intense error correction ability. Adding the benefits of multicarrier OFDM system and Reed Solomon codes to achieve the expected system performance. The coded OFDM system was modeled over and simulated using Matlab. The bit error rate (BER) and energy bit (Eb) per noise power density (No) was performed during system simulations. QPSK modulation was used to modulate the random bits. From the simulation results It can be seen that BER vs. EB/No parameter for Coded OFDM system lower than uncoded OFDM. This was because RS codes succeed to correcting the error generated along data transmission.

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5

Grolmusz, Vince. "Co-Orthogonal Codes." Designs, Codes and Cryptography 38, no. 3 (March 2006): 363–72. http://dx.doi.org/10.1007/s10623-005-1495-4.

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6

Chee, Yeow Meng, Han Mao Kiah, San Ling, and Hengjia Wei. "Geometric Orthogonal Codes of Size Larger Than Optical Orthogonal Codes." IEEE Transactions on Information Theory 64, no. 4 (April 2018): 2883–95. http://dx.doi.org/10.1109/tit.2017.2788140.

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7

Asif, Muhammad, Wuyang Zhou, Qingping Yu, Xingwang Li, and Nauman Ali Khan. "A Deterministic Construction for Jointly Designed Quasicyclic LDPC Coded-Relay Cooperation." Wireless Communications and Mobile Computing 2019 (September 26, 2019): 1–12. http://dx.doi.org/10.1155/2019/5249373.

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This correspondence presents a jointly designed quasicyclic (QC) low-density parity-check (LDPC) coded-relay cooperation with joint-iterative decoding in the destination node. Firstly, a design-theoretic construction of QC-LDPC codes based on a combinatoric design approach known as optical orthogonal codes (OOC) is presented. Proposed OOC-based construction gives three classes of binary QC-LDPC codes with no length-4 cycles by utilizing some known ingredients including binary matrix dispersion of elements of finite field, incidence matrices, and circulant decomposition. Secondly, the proposed OOC-based construction gives an effective method to jointly design length-4 cycles free QC-LDPC codes for coded-relay cooperation, where sum-product algorithm- (SPA-) based joint-iterative decoding is used to decode the corrupted sequences coming from the source or relay nodes in different time frames over constituent Rayleigh fading channels. Based on the theoretical analysis and simulation results, proposed QC-LDPC coded-relay cooperations outperform their competitors under same conditions over the Rayleigh fading channel with additive white Gaussian noise.

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8

Kim, Dong-Hoon, Hyung-Jung Kim, and Jae-Han Lim. "Design of Optimized Coded LFM Waveform for Spectrum Shared Radar System." Sensors 21, no. 17 (August 28, 2021): 5796. http://dx.doi.org/10.3390/s21175796.

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To meet the increasing demands for remote sensing, a number of radar systems using Linear Frequency Modulation (LFM) waveforms have been deployed, causing the problem of depleting frequency resources. To address this problem, several researchers have proposed the Spectrum Shared Radar System (SSRS) in which multiple radars share the same frequency band to transmit and receive their own signals. To mitigate the interferences caused by the signal transmission by other radars, SSRS employs orthogonal waveforms that inherit the orthogonality of the waveforms from orthogonal codes. However, the inherited orthogonality of the codes is significantly reduced when incorporating LFM waveforms with the codes. To solve this problem, in this paper, we propose a novel but simple scheme for generating a set of optimized coded LFM waveforms via new optimization framework. In the optimization framework, we minimize the weighted sum of autocorrelation sidelobe peaks (ASP) and cross-correlation peaks (CP) of the coded LFM waveforms to maximize the orthogonality of the waveforms. Through computer simulations, we show that the waveforms generated by the proposed scheme outperform the waveforms created by previous proposals in terms of ASP and CP.

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9

BASSA, Alp, and Nesrin TUTAŞ. "Extending self-orthogonal codes." TURKISH JOURNAL OF MATHEMATICS 43, no. 5 (September 28, 2019): 2177–82. http://dx.doi.org/10.3906/mat-1905-103.

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10

Gustavsson, B., and T. Grydeland. "Orthogonal-polarization alternating codes." Radio Science 44, no. 6 (December 2009): n/a. http://dx.doi.org/10.1029/2008rs004132.

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11

Noori Ghanim, Zainab, and Fadia Noori Hummadi Al-Nuaimy. "Variable length error correcting code for image in OFDM and PAPR reduction." Indonesian Journal of Electrical Engineering and Computer Science 27, no. 2 (August 1, 2022): 859. http://dx.doi.org/10.11591/ijeecs.v27.i2.pp859-866.

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Data <span>transmission in orthogonal frequency division multiplexing (OFDM) system needs source and channel coding, the transmitted data suffers from the bad effect of large peak to average power ratio (PAPR). Source code and channel codes can be joined using different joined codes. Variable length error correcting code (VLEC) is one of these joined codes. VLEC is used in mat lab simulation for image transmission in OFDM system, different VLEC code length is used and compared to find that the PAPR decreased with increasing the code length. Several techniques are used and compared for PAPR reduction. The PAPR of OFDM signal is measured for image coding with VLEC and compared with image coded by Huffman source coding and Bose-Chaudhuri-Hochquenghem (BCH) channel coding, the VLEC code decreases the data transmitted size and keep the same level of PAPR reduction with respect to data coded by Huffman and BCH code when using PAPR reduction methods.</span>

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12

Federer, Walter T., and John P. Mandeli. "Orthogonal F-rectangles, orthogonal arrays, and codes." Journal of Combinatorial Theory, Series A 43, no. 2 (November 1986): 149–64. http://dx.doi.org/10.1016/0097-3165(86)90057-9.

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13

Murad, Mohsin, Imran A. Tasadduq, and Pablo Otero. "Coded-GFDM for Reliable Communication in Underwater Acoustic Channels." Sensors 22, no. 7 (March 30, 2022): 2639. http://dx.doi.org/10.3390/s22072639.

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The performance of the coded generalized frequency division multiplexing (GFDM) transceiver has been evaluated in a shallow underwater acoustic channel (UAC). Acoustic transmission is the scheme of choice for communication in UAC since radio waves suffer from absorption and light waves scatter. Although orthogonal frequency division multiplexing (OFDM) has found its ground for multicarrier acoustic underwater communication, it suffers from high peak to average power ratio (PAPR) and out of band (OOB) emissions. We propose a coded-GFDM based multicarrier system since GFDM has a higher spectral efficiency compared to a traditional OFDM system. In doing so, we assess two block codes, namely Bose, Chaudari, and Hocquenghem (BCH) codes, Reed-Solomon (RS) codes, and several convolutional codes. We present the error performances of these codes when used with GFDM. Furthermore, we evaluate the performance of the proposed system using two equalizers: Matched Filter (MF) and Zero-Forcing (ZF). Simulation results show that among the various block coding schemes that we tested, BCH (31,6) and RS (15,3) give the best error performance. Among the convolutional codes that we tested, rate 1/4 convolutional codes give the best performance. However, the performance of BCH and RS codes is much better than the convolutional codes. Moreover, the performance of the ZF equalizer is marginally better than the MF equalizer. In conclusion, using the channel coding schemes with GFDM improves error performance manifolds thereby increasing the reliability of the GFDM system despite slightly higher complexity.

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14

Geng, Fu Quan, Zhi Gang Huang, Xuan Jie Ning, and Mao Fan Yang. "A Joint Improved Irregular Accumulate Concatenated Tree Coding and Frequency Hopping OFDM Modulation Scheme for Wireless Networks." Advanced Materials Research 902 (February 2014): 364–69. http://dx.doi.org/10.4028/www.scientific.net/amr.902.364.

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Joint channel coding and spread spectrum modulation technologies bring to wireless networks the tremendous amount of performance improvement, the elimination, and the mitigation of interference. This paper proposes an improved design for irregular accumulate concatenated tree (IACT) codes, which can be viewed as simply precoded by an accumulator. This class of codes belongs to the special turbo-like codes, which combines the advantages of fast encoder structures of turbo codes, and the advantages of parallel high-speed belief-propagation (BP) iterative decoding algorithm of low-density parity-check (LDPC) codes. The improved IACT codes can be coded via a Tanner graph. With these improved codes, we propose a joint IACT coding and frequency hopping orthogonal frequency division multiplexing (FH-OFDM) modulation scheme for wireless networks. We compare the performance of different coding bases such as the irregular concatenated tree (ICT) codes and turbo codes in the scheme by theoretical analysis and simulation. Numerical results are shown that the proposed scheme with these IACT codes has really good performance.

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15

Teimouri, M., A. Hedayat, and M. Shiva. "Concatenated bit-interleaved coded modulation and orthogonal space-time block codes over fading channels." IET Communications 3, no. 8 (2009): 1354. http://dx.doi.org/10.1049/iet-com.2008.0477.

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16

Lisoněk, Petr, and Vijaykumar Singh. "Quantum codes from nearly self-orthogonal quaternary linear codes." Designs, Codes and Cryptography 73, no. 2 (February 21, 2014): 417–24. http://dx.doi.org/10.1007/s10623-014-9934-8.

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17

Durğun, Yilmaz. "Extended maximal self-orthogonal codes." Discrete Mathematics, Algorithms and Applications 11, no. 05 (October 2019): 1950052. http://dx.doi.org/10.1142/s1793830919500526.

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Self-dual and maximal self-orthogonal codes over [Formula: see text], where [Formula: see text] is even or [Formula: see text](mod 4), are extensively studied in this paper. We prove that every maximal self-orthogonal code can be extended to a self-dual code as in the case of binary Golay code. Using these results, we show that a self-dual code can also be constructed by gluing theory even if the sum of the lengths of the gluing components is odd. Furthermore, the (Hamming) weight enumerator [Formula: see text] of a self-dual code [Formula: see text] is given in terms of a maximal self-orthogonal code [Formula: see text], where [Formula: see text] is obtained by the extension of [Formula: see text].

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18

Mazurkov, M. I., and M. Yu Gerasimenko. "Operation algorithms and block diagrams of codecs of orthogonal codes based on perfect binary arrays." Radioelectronics and Communications Systems 50, no. 12 (December 2007): 674–79. http://dx.doi.org/10.3103/s0735272707120047.

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19

Mehry, Shahram. "On quantum codes from codes over Rm." Revista Colombiana de Matemáticas 56, no. 1 (November 2, 2022): 77–91. http://dx.doi.org/10.15446/recolma.v56n1.105620.

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Let Rm = Fq [y] = /〈ym - 1〉, where m|q - 1. In this paper, we obtain the structure of linear and cyclic codes over Rm. Also, we introduce a preserving-orthogonality Gray map from Rm to Fmq. Among the main results, we obtain the exact structure of self-orthogonal cyclic codes over Rm to introduce parameters of quantum codes from cyclic codes over Rm.

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20

QIAN, JIANFA, WENPING MA, and XINMEI WANG. "QUANTUM ERROR-CORRECTING CODES FROM QUASI-CYCLIC CODES." International Journal of Quantum Information 06, no. 06 (December 2008): 1263–69. http://dx.doi.org/10.1142/s0219749908004444.

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Quasi-cyclic codes form a generalization of cyclic codes, and contain a large number of record breaking codes. In this paper, we provide a method for constructing self-orthogonal quasi-cyclic codes, and obtain a large number of new quantum quasi-cyclic codes by CSS construction.

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21

Guan, Chaofeng, Ruihu Li, Hao Song, Liangdong Lu, and Husheng Li. "Ternary quantum codes constructed from extremal self-dual codes and self-orthogonal codes." AIMS Mathematics 7, no. 4 (2022): 6516–34. http://dx.doi.org/10.3934/math.2022363.

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<abstract><p>In this paper, we consider $ S $-chains of extremal self-dual and self-orthogonal codes and their applications in the construction of quantum codes. Then, by virtue of covering radius, we determine necessary conditions for linear codes to have subcodes with large dual distances and design a new $ S $-chain search method. As computational results, 18 $ S $-chains with large distances are obtained, and many good quantum codes can be derived from those $ S $-chains by Steane construction, some of which improve the previous results.</p></abstract>

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22

Singh, Abhay Kumar, Narendra Kumar, and Kar Ping Shum. "Cyclic self-orthogonal codes over finite chain ring." Asian-European Journal of Mathematics 11, no. 06 (December 2018): 1850078. http://dx.doi.org/10.1142/s179355711850078x.

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In this paper, we study the cyclic self-orthogonal codes over a finite commutative chain ring [Formula: see text], where [Formula: see text] is a prime number. A generating polynomial of cyclic self-orthogonal codes over [Formula: see text] is obtained. We also provide a necessary and sufficient condition for the existence of nontrivial self-orthogonal codes over [Formula: see text]. Finally, we determine the number of the above codes with length [Formula: see text] over [Formula: see text] for any [Formula: see text]. The results are given by Zhe-Xian Wan on cyclic codes over Galois rings in [Z. Wan, Cyclic codes over Galois rings, Algebra Colloq. 6 (1999) 291–304] are extended and strengthened to cyclic self-orthogonal codes over [Formula: see text].

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23

Wu, Yansheng, and Yoonjin Lee. "Binary LCD Codes and Self-Orthogonal Codes via Simplicial Complexes." IEEE Communications Letters 24, no. 6 (June 2020): 1159–62. http://dx.doi.org/10.1109/lcomm.2020.2982381.

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24

El-Mesady, A., Y. S. Hamed, and Khadijah M. Abualnaja. "A novel application on mutually orthogonal graph squares and graph-orthogonal arrays." AIMS Mathematics 7, no. 5 (2022): 7349–73. http://dx.doi.org/10.3934/math.2022410.

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<abstract> <p>Security of personal information has become a major concern due to the increasing use of the Internet by individuals in the digital world. The main purpose here is to prevent an unauthorized person from gaining access to confidential information. The solution to such a problem is by authentication of users. Authentication has a very important role in achieving security. Mutually orthogonal graph squares (MOGS) are considered the generalization of mutually orthogonal Latin squares (MOLS). Also, MOGS are generated from edge decompositions of complete bipartite graphs by isomorphic graphs. Graph-orthogonal arrays can be constructed by MOGS. In this paper, graph-orthogonal arrays are used for constructing authentication codes. These arrays are the encoding matrices of authentication tags. We introduce the concepts and basic theorems of MOGS, graph-orthogonal arrays, and authentication codes. After constructing graph-orthogonal arrays by MOGS, then there is an established mapping between graph-orthogonal arrays and message set. This manages us to construct perfect non-splitting and splitting Cartesian authentication codes. In both cases, we calculate the probabilities of successful impersonation attacks and substitution attacks. Besides that, the performance of constructed non-splitting and splitting authentication codes is analyzed. In the end, optimal authentication codes and secure authentication codes are constructed.</p> </abstract>

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25

QIAN, JIANFA, WENPING MA, and WANGMEI GUO. "QUANTUM CODES FROM CYCLIC CODES OVER FINITE RING." International Journal of Quantum Information 07, no. 06 (September 2009): 1277–83. http://dx.doi.org/10.1142/s0219749909005560.

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A new method to obtain self-orthogonal codes over finite field F2 is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F2 + uF2. As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F2 + uF2.

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26

Sahni, Amita, and Poonam Trama Sehgal. "Hermitian Self-Orthogonal Constacyclic Codes over Finite Fields." Journal of Discrete Mathematics 2014 (November 12, 2014): 1–7. http://dx.doi.org/10.1155/2014/985387.

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Necessary and sufficient conditions for the existence of Hermitian self-orthogonal constacyclic codes of length n over a finite field Fq2, n coprime to q, are found. The defining sets and corresponding generator polynomials of these codes are also characterised. A formula for the number of Hermitian self-orthogonal constacyclic codes of length n over a finite field Fq2 is obtained. Conditions for the existence of numerous MDS Hermitian self-orthogonal constacyclic codes are obtained. The defining set and the number of such MDS codes are also found.

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27

Samanta, Supriti, Goutam K. Maity, and Subhadipta Mukhopadhyay. "Implementation of Orthogonal Codes Using MZI." Micro and Nanosystems 12, no. 3 (December 1, 2020): 159–67. http://dx.doi.org/10.2174/1876402912666200211121624.

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Background: In Code Division Multiple Access (CDMA)/Multi-Carrier CDMA (MCCDMA), Walsh-Hadamard codes are widely used for its orthogonal characteristics, and hence, it leads to good contextual connection property. These orthogonal codes are important because of their various significant applications. Objective: To use the Mach–Zehnder Interferometer (MZI) for all-optical Walsh-Hadamard codes is implemented in this present paper. Method: The Mach–Zehnder Interferometer (MZI) is considered for the Tree architecture of Semiconductor Optical Amplifier (SOA). The second-ordered Hadamard and the inverse Hadamard matrix are constructed using SOA-MZIs. Higher-order Hadamard matrix (H4) formed by the process of Kronecker product with lower-order Hadamard matrix (H2) is also analyzed and constructed. Results: To experimentally get the result from these schemes, some design issues e,g Time delay, nonlinear phase modulation, extinction ratio, and synchronization of signals are the important issues. Lasers of wavelength 1552 nm and 1534 nm can be used as input and control signals, respectively. As the whole system is digital, intensity losses due to couplers in the interconnecting stage may not create many problems in producing the desired optical bits at the output. The simulation results were obtained by Matlab-9. Here, Hadamard H2 (2×2) matrix output beam intensity (I ≈ 108 w.m-2) for different values of inputs. Conclusion: Implementation of Walsh-Hadamard codes using MZI is explored in this paper, and experimental results show the better performance of the proposed scheme compared to recently reported methods using electronic circuits regarding the issues of versatility, reconfigurability, and compactness. The design can be used and extended for diverse applications for which Walsh-Hadamard codes are required.

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28

Jafarkhani, H., and N. Seshadri. "Super-orthogonal space-time trellis codes." IEEE Transactions on Information Theory 49, no. 4 (April 2003): 937–50. http://dx.doi.org/10.1109/tit.2003.809607.

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Fang, Xiaolei, Meiqing Liu, and Jinquan Luo. "New MDS Euclidean Self-Orthogonal Codes." IEEE Transactions on Information Theory 67, no. 1 (January 2021): 130–37. http://dx.doi.org/10.1109/tit.2020.3020986.

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30

Argon, Cenk. "Semi-randomly constructed optical orthogonal codes." Optics Communications 282, no. 4 (February 2009): 500–503. http://dx.doi.org/10.1016/j.optcom.2008.10.043.

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Ren, Tian, Yong Guan, Erry Gunawan, and Er Zhang. "Shift-orthogonal space-time block codes." IEEE Transactions on Communications 58, no. 6 (June 2010): 1605–9. http://dx.doi.org/10.1109/tcomm.2010.06.090054.

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32

Chang, Yanxun, and Ying Miao. "Constructions for optimal optical orthogonal codes." Discrete Mathematics 261, no. 1-3 (January 2003): 127–39. http://dx.doi.org/10.1016/s0012-365x(02)00464-8.

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33

Pott, Alexander. "A note on self-orthogonal codes." Discrete Mathematics 76, no. 3 (1989): 283–84. http://dx.doi.org/10.1016/0012-365x(89)90327-0.

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34

Cardinali, Ilaria, and Luca Giuzzi. "Codes and caps from orthogonal Grassmannians." Finite Fields and Their Applications 24 (November 2013): 148–69. http://dx.doi.org/10.1016/j.ffa.2013.07.003.

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35

Fu, Wenqing, and Tao Feng. "On self-orthogonal group ring codes." Designs, Codes and Cryptography 50, no. 2 (July 2, 2008): 203–14. http://dx.doi.org/10.1007/s10623-008-9224-4.

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36

Wassermann, Alfred, and Axel Kohnert. "Construction of self-orthogonal linear codes." Electronic Notes in Discrete Mathematics 27 (October 2006): 105. http://dx.doi.org/10.1016/j.endm.2006.08.077.

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37

Guo, Luobin, Yuena Ma, and Youqian Feng. "Quantum Codes Constructed from Self-Dual Codes and Maximal Self-Orthogonal Codes Over F5." Procedia Engineering 29 (2012): 3448–53. http://dx.doi.org/10.1016/j.proeng.2012.01.510.

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38

Ashraf, Mohammad, and Ghulam Mohammad. "Quantum codes from cyclic codes over F3 + vF3." International Journal of Quantum Information 12, no. 06 (September 2014): 1450042. http://dx.doi.org/10.1142/s0219749914500427.

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Let R = F3 + vF3 be a finite commutative ring, where v2 = 1. It is a finite semi-local ring, not a chain ring. In this paper, we give a construction for quantum codes from cyclic codes over R. We derive self-orthogonal codes over F3 as Gray images of linear and cyclic codes over R. In particular, we use two codes associated with a cyclic code over R of arbitrary length to determine the parameters of the corresponding quantum code.

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Wu, Yansheng, and Yoonjin Lee. "Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication." Mathematics 8, no. 9 (September 3, 2020): 1495. http://dx.doi.org/10.3390/math8091495.

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It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n≥7. We also find some (almost) “optimal” quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.

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40

Gan, Chunyu, Chengju Li, Sihem Mesnager, and Haifeng Qian. "On Hulls of Some Primitive BCH Codes and Self-Orthogonal Codes." IEEE Transactions on Information Theory 67, no. 10 (October 2021): 6442–55. http://dx.doi.org/10.1109/tit.2021.3076878.

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41

SHEN, Lin-Zhi. "New Asymptotically Optimal Optical Orthogonal Signature Pattern Codes from Cyclic Codes." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E102.A, no. 10 (October 1, 2019): 1416–19. http://dx.doi.org/10.1587/transfun.e102.a.1416.

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42

Gao, Yanyan, Qin Yue, and Yansheng Wu. "LCD Codes and Self-orthogonal Codes in Finite Dihedral Group Algebras." Chinese Annals of Mathematics, Series B 42, no. 5 (September 2021): 791–800. http://dx.doi.org/10.1007/s11401-021-0291-4.

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43

Zhou, Zhengchun, Xia Li, Chunming Tang, and Cunsheng Ding. "Binary LCD Codes and Self-Orthogonal Codes From a Generic Construction." IEEE Transactions on Information Theory 65, no. 1 (January 2019): 16–27. http://dx.doi.org/10.1109/tit.2018.2823704.

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44

Cardinal, Christian, Eric Roy, and David Haccoun. "Simplified convolutional self-doubly orthogonal codes: search algorithms and codes determination." IEEE Transactions on Communications 57, no. 6 (June 2009): 1674–82. http://dx.doi.org/10.1109/tcomm.2009.06.070529.

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45

Shah, H., A. Hedayat, and A. Nosratinia. "Performance of concatenated channel codes and orthogonal space-time block codes." IEEE Transactions on Wireless Communications 5, no. 6 (June 2006): 1406–14. http://dx.doi.org/10.1109/twc.2006.1638661.

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46

Gao, Yanyan, Qin Yue, and Yansheng Wu. "LCD codes and self-orthogonal codes in generalized dihedral group algebras." Designs, Codes and Cryptography 88, no. 11 (July 2, 2020): 2275–87. http://dx.doi.org/10.1007/s10623-020-00778-z.

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47

Alahmadi, Adel, Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez, and Patrick Solé. "Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four." Mathematics 11, no. 23 (November 23, 2023): 4736. http://dx.doi.org/10.3390/math11234736.

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Abstract:

We study the structure of self-orthogonal and self-dual codes over two non-unital rings of order four, namely, the commutative ring I=a,b|2a=2b=0,a2=b,ab=0 and the noncommutative ring E=a,b|2a=2b=0,a2=a,b2=b,ab=a,ba=b. We use these structures to give mass formulas for self-orthogonal and self-dual codes over these two rings, that is, we give the formulas for the number of inequivalent self-orthogonal and self-dual codes, of a given type, over the said rings. Finally, using the mass formulas, we classify self-orthogonal and self-dual codes over each ring, for small lengths and types.

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48

Bouyuklieva, Stefka. "Shortened and punctured codes." Annual of Konstantin Preslavsky University of Shumen, Faculty of mathematics and informatics XXIV C (2023): 3–7. http://dx.doi.org/10.46687/htwu8165.

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49

Dhawan, Priya, and Narinder Sharma. "Pre-coded Orthogonal Space-Time Block Codes over MIMO Channel and its Analysis for Antenna Selection Technique." International Journal of Computer Applications 103, no. 9 (October 18, 2014): 30–33. http://dx.doi.org/10.5120/18104-9202.

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50

Dertli, Abdullah, Yasemin Cengellenmis, and Senol Eren. "On quantum codes obtained from cyclic codes over A2." International Journal of Quantum Information 13, no. 03 (April 2015): 1550031. http://dx.doi.org/10.1142/s0219749915500318.

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Abstract:

In this paper, quantum codes from cyclic codes over A2 = F2 + uF2 + vF2 + uvF2, u2 = u, v2 = v, uv = vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A2, then so is Ψ(C), where Ψ is a Gray map. A necessary and sufficient condition for cyclic codes over A2 that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A2.

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