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Journal articles on the topic 'Coding theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 21 September 2024

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1

Stine, Robert A. "Coding theory." Wiley Interdisciplinary Reviews: Computational Statistics 1, no. 3 (November 2009): 261–70. http://dx.doi.org/10.1002/wics.42.

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2

Greferath, Marcus, Camilla Hollanti, and Joachim Rosenthal. "Contemporary Coding Theory." Oberwolfach Reports 16, no. 1 (February 26, 2020): 773–840. http://dx.doi.org/10.4171/owr/2019/13.

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3

van Lint, J. H. "Coding theory introduction." IEEE Transactions on Information Theory 34, no. 5 (September 1988): 1274–75. http://dx.doi.org/10.1109/tit.1988.8862503.

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4

SAKATA, Shojiro. "Algebraic Coding Theory." IEICE ESS Fundamentals Review 1, no. 3 (2008): 3_44–3_57. http://dx.doi.org/10.1587/essfr.1.3_44.

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5

Ohashi, Masayoshi, and Toshio Mizuno. "Introduction to Coding Theory(15); Application of Coding Theory Satellite Communication." Journal of the Institute of Television Engineers of Japan 45, no. 10 (1991): 1291–96. http://dx.doi.org/10.3169/itej1978.45.1291.

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6

Baylis, John, D. G. Hoffman, D. A. Leonard, C. C. Lindner, K. T. Phelps, C. A. Rodger, and J. R. Wall. "Coding Theory: The Essentials." Mathematical Gazette 77, no. 480 (November 1993): 381. http://dx.doi.org/10.2307/3619794.

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7

Anderson, Ian, and J. H. van Lint. "Introduction to Coding Theory." Mathematical Gazette 77, no. 480 (November 1993): 383. http://dx.doi.org/10.2307/3619795.

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8

Baylis, John, Gareth A. Jones, and J. Mary Jones. "Information and Coding Theory." Mathematical Gazette 85, no. 503 (July 2001): 377. http://dx.doi.org/10.2307/3622076.

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9

Dawy, Zaher, Pavol Hanus, Johanna Weindl, Janis Dingel, and Faruck Morcos. "On genomic coding theory." European Transactions on Telecommunications 18, no. 8 (2007): 873–79. http://dx.doi.org/10.1002/ett.1201.

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10

Saito, Minoru. "Introduction to Coding Theory: (14) Application of Coding Theory to Computer Technology." Journal of the Institute of Television Engineers of Japan 45, no. 9 (1991): 1089–94. http://dx.doi.org/10.3169/itej1978.45.1089.

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11

Tanaka, Kunimaro. "Introduction to Coding Theory (14);Application of Coding Theory to Digital Audio." Journal of the Institute of Television Engineers of Japan 45, no. 7 (1991): 837–44. http://dx.doi.org/10.3169/itej1978.45.837.

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12

Yamada, Osamu. "Introduction to Coding Theory; (13) Applications of Coding Theory to Broadcasting Technology." Journal of the Institute of Television Engineers of Japan 45, no. 8 (1991): 970–80. http://dx.doi.org/10.3169/itej1978.45.970.

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13

Yeung, Raymond W., Shuo-Yen Robert Li, Ning Cai, and Zhen Zhang. "Network Coding Theory: Single Sources." Foundations and Trends® in Communications and Information Theory 2, no. 4 (2005): 241–329. http://dx.doi.org/10.1561/0100000007i.

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14

Ball, Taylor, Eduardo Camps, Henry Chimal-Dzul, Delio Jaramillo-Velez, Hiram López, Nathan Nichols, Matthew Perkins, Ivan Soprunov, German Vera-Martínez, and Gwyn Whieldon. "Coding theory package for Macaulay2." Journal of Software for Algebra and Geometry 11, no. 1 (December 31, 2021): 113–22. http://dx.doi.org/10.2140/jsag.2021.11.113.

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15

Raigorodskii, A. M. "Combinatorial Geometry and Coding Theory*." Fundamenta Informaticae 145, no. 3 (August 19, 2016): 359–69. http://dx.doi.org/10.3233/fi-2016-1365.

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16

MATSUI, Hajime. "Algebraic Methods in Coding Theory." IEICE ESS Fundamentals Review 8, no. 3 (2015): 151–61. http://dx.doi.org/10.1587/essfr.8.151.

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17

Delsarte, P., and V. I. Levenshtein. "Association schemes and coding theory." IEEE Transactions on Information Theory 44, no. 6 (1998): 2477–504. http://dx.doi.org/10.1109/18.720545.

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18

Savari, S. A. "Renewal theory and source coding." Proceedings of the IEEE 88, no. 11 (November 2000): 1692–702. http://dx.doi.org/10.1109/5.892705.

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19

Ginosar, Yuval, and Aviram Rochas Moreno. "Crossed Products and Coding Theory." IEEE Transactions on Information Theory 65, no. 10 (October 2019): 6224–33. http://dx.doi.org/10.1109/tit.2019.2923652.

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20

Ning Cai and T. Chan. "Theory of Secure Network Coding." Proceedings of the IEEE 99, no. 3 (March 2011): 421–37. http://dx.doi.org/10.1109/jproc.2010.2094592.

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21

Dougherty, R., C. Freiling, and K. Zeger. "Network Coding and Matroid Theory." Proceedings of the IEEE 99, no. 3 (March 2011): 388–405. http://dx.doi.org/10.1109/jproc.2010.2095490.

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22

Maruta, Tatsuya, Isao Kikumasa, and Hitoshi Kaneta. "Singleton arrays in coding theory." Bulletin of the Australian Mathematical Society 37, no. 3 (June 1988): 333–35. http://dx.doi.org/10.1017/s0004972700026940.

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23

Aarts, Emile H. L., and Peter J. M. van Laarhoven. "Local search in coding theory." Discrete Mathematics 106-107 (September 1992): 11–18. http://dx.doi.org/10.1016/0012-365x(92)90524-j.

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24

Yeung, Raymond W. "Network coding theory: An introduction." Frontiers of Electrical and Electronic Engineering in China 5, no. 3 (August 5, 2010): 363–90. http://dx.doi.org/10.1007/s11460-010-0103-1.

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25

Etzion, T., and L. Storme. "Galois geometries and coding theory." Designs, Codes and Cryptography 78, no. 1 (December 11, 2015): 311–50. http://dx.doi.org/10.1007/s10623-015-0156-5.

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26

Blake, Ian F. "A perspective on coding theory." Information Sciences 57-58 (September 1991): 111–18. http://dx.doi.org/10.1016/0020-0255(91)90070-b.

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27

Clark, James M., and Allan Paivio. "Dual coding theory and education." Educational Psychology Review 3, no. 3 (September 1991): 149–210. http://dx.doi.org/10.1007/bf01320076.

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28

Borst, Alexander, and Frédéric E. Theunissen. "Information theory and neural coding." Nature Neuroscience 2, no. 11 (November 1999): 947–57. http://dx.doi.org/10.1038/14731.

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29

Bassoli, Riccardo, Hugo Marques, Jonathan Rodriguez, Kenneth W. Shum, and Rahim Tafazolli. "Network Coding Theory: A Survey." IEEE Communications Surveys & Tutorials 15, no. 4 (2013): 1950–78. http://dx.doi.org/10.1109/surv.2013.013013.00104.

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30

Guerreiro, Marinês. "Group algebras and coding theory." São Paulo Journal of Mathematical Sciences 10, no. 2 (May 9, 2016): 346–71. http://dx.doi.org/10.1007/s40863-016-0040-x.

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31

SURER, PAUL. "Coding of substitution dynamical systems as shifts of finite type." Ergodic Theory and Dynamical Systems 36, no. 3 (November 6, 2014): 944–72. http://dx.doi.org/10.1017/etds.2014.80.

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We develop a theory that allows us to code dynamical systems induced by primitive substitutions continuously as shifts of finite type in many different ways. The well-known prefix–suffix coding turns out to correspond to one special case. We precisely analyse the basic properties of these codings (injectivity, coding of the periodic points, properties of the presentation graph, interaction with the shift map). A lot of examples illustrate the theory and show that, depending on the particular coding, several amazing effects may occur. The results give new insights into the theory of substitution dynamical systems and might serve as a powerful tool for further researches.

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32

Alon, Noga, and Andy Liu. "An Application of Set Theory to Coding Theory." Mathematics Magazine 62, no. 4 (October 1, 1989): 233. http://dx.doi.org/10.2307/2689761.

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33

Alon, Noca, and Andy Liu. "An Application of Set Theory to Coding Theory." Mathematics Magazine 62, no. 4 (October 1989): 233–37. http://dx.doi.org/10.1080/0025570x.1989.11977444.

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34

Yan, Shan Jun. "Study on Shannon Source-Coding Theory." Applied Mechanics and Materials 687-691 (November 2014): 4158–62. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.4158.

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This pape analyzed the essence of Shannon source coding theory, and put forward the concept of utilization rate of source symbols, then by using this concept a new description for lossless source coding theory of Shannon was gave, from a new perspective the essence of Shannon source coding theory was identified.

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35

Rebelatto, João Luiz, Bartolomeu F. Uchoa-Filho, Yonghui Li, and Branka Vucetic. "Multiuser Cooperative Diversity Through Network Coding Based on Classical Coding Theory." IEEE Transactions on Signal Processing 60, no. 2 (February 2012): 916–26. http://dx.doi.org/10.1109/tsp.2011.2174787.

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36

Konopka, Andrzej K. "Theory of degenerate coding and informational parameters of protein coding genes." Biochimie 67, no. 5 (May 1985): 455–68. http://dx.doi.org/10.1016/s0300-9084(85)80264-9.

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37

Imai, Hideki. "Technical Guide. Introduction to Coding Theory (End); Future Trend of Coding." Journal of the Institute of Television Engineers of Japan 45, no. 11 (1991): 1423–31. http://dx.doi.org/10.3169/itej1978.45.1423.

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38

Mimura, Kazushi. "Theory of Neural Networks and Coding." Brain & Neural Networks 13, no. 1 (2006): 19–27. http://dx.doi.org/10.3902/jnns.13.19.

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39

Hamming, Richard, and Raymond Hill. "A First Course in Coding Theory." American Mathematical Monthly 95, no. 8 (October 1988): 786. http://dx.doi.org/10.2307/2322277.

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40

Crilly, Tony, and Raymond Hill. "A First Course in Coding Theory." Mathematical Gazette 72, no. 459 (March 1988): 72. http://dx.doi.org/10.2307/3618021.

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41

Prasad, Bandhu. "Coding theory based on balancing polynomials." Control and Cybernetics 50, no. 2 (June 1, 2021): 335–46. http://dx.doi.org/10.2478/candc-2021-0017.

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Abstract In this paper, we introduce a Q 2 n ( x ) Q_2^n\left( x \right) matrix, whose elements are balancing polynomials, and develop a new coding and decoding method following from the Q 2 n ( x ) Q_2^n\left( x \right) matrix. We establish the relations between the code matrix elements, error detection and correction for this coding theory.

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42

Baylis, John, D. R. Hankerson, D. G. Hoffman, D. A. Leonard, C. C. Lindner, K. T. Phelps, C. A. Rodger, and J. R. Wall. "Coding Theory and Cryptography: The Essentials." Mathematical Gazette 85, no. 504 (November 2001): 561. http://dx.doi.org/10.2307/3621814.

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43

., Ayten Ozkan, and E. Mehmet Ozkan . "A Different Approach to Coding Theory." Journal of Applied Sciences 2, no. 11 (October 15, 2002): 1032–33. http://dx.doi.org/10.3923/jas.2002.1032.1033.

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44

Gassner, Niklas, Marcus Greferath, Joachim Rosenthal, and Violetta Weger. "Bounds for Coding Theory over Rings." Entropy 24, no. 10 (October 16, 2022): 1473. http://dx.doi.org/10.3390/e24101473.

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Coding theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. It has been well established that, with the generalization of the algebraic structure to rings, there is a need to also generalize the underlying metric beyond the usual Hamming weight used in traditional coding theory over finite fields. This paper introduces a generalization of the weight introduced by Shi, Wu and Krotov, called overweight. Additionally, this weight can be seen as a generalization of the Lee weight on the integers modulo 4 and as a generalization of Krotov's weight over the integers modulo 2s for any positive integer s. For this weight, we provide a number of well-known bounds, including a Singleton bound, a Plotkin bound, a sphere-packing bound and a Gilbert–Varshamov bound. In addition to the overweight, we also study a well-known metric on finite rings, namely the homogeneous metric, which also extends the Lee metric over the integers modulo 4 and is thus heavily connected to the overweight. We provide a new bound that has been missing in the literature for homogeneous metric, namely the Johnson bound. To prove this bound, we use an upper estimate on the sum of the distances of all distinct codewords that depends only on the length, the average weight and the maximum weight of a codeword. An effective such bound is not known for the overweight.

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45

Kashyap, Anil Kumar. "Planar Near-Rings And Coding Theory." IOSR Journal of Mathematics 4, no. 6 (2013): 77–80. http://dx.doi.org/10.9790/5728-0467780.

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46

Haikin, Marina, Matan Gavish, Dustin G. Mixon, and Ram Zamir. "Asymptotic Frame Theory for Analog Coding." Foundations and Trends® in Communications and Information Theory 18, no. 4 (2021): 526–645. http://dx.doi.org/10.1561/0100000125.

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47

Xin Zhang, Jun Chen, S. B. Wicker, and T. Berger. "Successive Coding in Multiuser Information Theory." IEEE Transactions on Information Theory 53, no. 6 (June 2007): 2246–54. http://dx.doi.org/10.1109/tit.2007.896857.

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48

Cohen, G. D., S. Litsyn, and C. Zemor. "On greedy algorithms in coding theory." IEEE Transactions on Information Theory 42, no. 6 (1996): 2053–57. http://dx.doi.org/10.1109/18.556707.

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49

Kieffer, J. C. "Sample converses in source coding theory." IEEE Transactions on Information Theory 37, no. 2 (March 1991): 263–68. http://dx.doi.org/10.1109/18.75241.

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50

Joyner, David, and Robert Miller. "SAGE and coding theory (abstract only)." ACM Communications in Computer Algebra 42, no. 1-2 (July 25, 2008): 74–78. http://dx.doi.org/10.1145/1394042.1394085.

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