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Journal articles on the topic 'Cyclic matrice'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Uygun, Hilmiye Deniz Ertugrul, Nihat Tinkilic, Azade Attar, and Ibrahim Isildak. "Development of Potentiometric Lactate Biosensor Based on Composite pH Sensor." Journal of New Materials for Electrochemical Systems 19, no. 3 (September 20, 2016): 151–56. http://dx.doi.org/10.14447/jnmes.v19i3.313.

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In this study, a micro-sized lactate sensitive biosensor based on polyvinylchloride, quinhydrone and graphite composite pH sensing platform was developed. Lactate oxidase was immobilized on the composite layer as the biorecognition element. Transformation reaction of lactate to pyruvate and hydrogen peroxide was the basis of this biosensor system. In the reaction, hydrogen peroxide undergoes to give hydronium ions into solution, and the pH sensitive membrane detects the adjunct hydronium ions potentiometrically. The surface of lactate biosensor based composite pH sensing matrice was first examined for electrochemical elucidation by using cyclic voltammetry and electrochemical impedance spectroscopy. A linear response in concentration range from 5x10-5 to 1x10-1 mol/L was obtained with a detec-tion limit of 2x10-5 mol/L. The lactate biosensor developed was successfully applied for highly precise and efficient determination of lactate in food preparations. The biosensor exhibited a fast response time (10 s), had good stability, and had an extended lifetime.

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2

Tarasov, Vitaly. "Cyclic monodromy matrices forsl(n) trigonometricR-matrices." Communications in Mathematical Physics 158, no. 3 (December 1993): 459–83. http://dx.doi.org/10.1007/bf02096799.

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3

Shinjo, Masato, Tan Wang, Masashi Iwasaki, and Yoshimasa Nakamura. "Roots of Characteristic Polynomial Sequences in Iterative Block Cyclic Reductions." Mathematics 9, no. 24 (December 12, 2021): 3213. http://dx.doi.org/10.3390/math9243213.

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The block cyclic reduction method is a finite-step direct method used for solving linear systems with block tridiagonal coefficient matrices. It iteratively uses transformations to reduce the number of non-zero blocks in coefficient matrices. With repeated block cyclic reductions, non-zero off-diagonal blocks in coefficient matrices incrementally leave the diagonal blocks and eventually vanish after a finite number of block cyclic reductions. In this paper, we focus on the roots of characteristic polynomials of coefficient matrices that are repeatedly transformed by block cyclic reductions. We regard each block cyclic reduction as a composition of two types of matrix transformations, and then attempt to examine changes in the existence range of roots. This is a block extension of the idea presented in our previous papers on simple cyclic reductions. The property that the roots are not very scattered is a key to accurately solve linear systems in floating-point arithmetic. We clarify that block cyclic reductions do not disperse roots, but rather narrow their distribution, if the original coefficient matrix is symmetric positive or negative definite.

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4

Zheng, Yanpeng, and Xiaoyu Jiang. "Quasi-cyclic displacement and inversion decomposition of a quasi-Toeplitz matrix." AIMS Mathematics 7, no. 7 (2022): 11647–62. http://dx.doi.org/10.3934/math.2022649.

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<abstract><p>We study a class of column upper-minus-lower (CUML) Toeplitz matrices, which are "close" to the Toeplitz matrices in the sense that their ($ 1, -1 $)-cyclic displacements coincide with $ \varphi $-cyclic displacement of some Toeplitz matrices. Among others, we derive the inverse formula for CUML Toeplitz matrices in the form of sums of products of factor circulants by constructing the corresponding displacement of the matrices. In addition, by the relationship between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula for CUML Hankel matrices is also obtained.</p></abstract>

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5

Neumann, Peter M., and Cheryl E. Praeger. "Cyclic Matrices Over Finite Fields." Journal of the London Mathematical Society 52, no. 2 (October 1995): 263–84. http://dx.doi.org/10.1112/jlms/52.2.263.

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6

Tam, Bit-Shun. "On matrices with cyclic structure." Linear Algebra and its Applications 302-303 (December 1999): 377–410. http://dx.doi.org/10.1016/s0024-3795(99)00097-x.

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7

Riaza, Ricardo. "Cyclic matrices of weighted digraphs." Discrete Applied Mathematics 160, no. 3 (February 2012): 280–90. http://dx.doi.org/10.1016/j.dam.2011.09.005.

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8

Sergeev, A. "Interrelation of Symmetry and Antisymmetry of Quasi-Orthogonal Cyclic Matrices with Prime Numbers." Proceedings of Telecommunication Universities 8, no. 4 (January 5, 2023): 14–19. http://dx.doi.org/10.31854/1813-324x-2022-8-4-14-19.

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Quasi-orthogonal Hadamard matrices and Mersenne matrices with two and three values of the elements, used in digital data processing, are considered, as well as the basis of error-correcting codes and algorithms for transforming orthogonal images. Attention is paid to the structures of cyclic matrices with symmetries and antisymmetries. The connection between symmetry and antisymmetry of structures of cyclic Hadamard and Mersenne matrices on a orders equal to prime numbers, products of close primes, composite numbers, powers of a prime number is shown. Separately, orders equal to the degrees of the prime number 2 are distinguished, both the orders of Hadamard matrices and the basis of the composite orders of Mersenne matrices of block structures with two element values. It is shown that symmetric Hadamard matrices of cyclic and bicyclic structures, according to the extended Riser boundary, do not exist on orders above 32. Mersenne matrices of composite orders belonging to the sequence of Mersenne numbers 2k ‒ 1 nested in the sequence of orders of the main family of Mersenne matrices 4t ‒ 1 exist in a symmetric and antisymmetric form. For orders equal to the powers of a prime number, Mersenne matrices exist in the form of block-diagonal constructions with three element values. The value of prime power determines the number of blocks along the diagonal of the matrix on which the elements with the third value are located. The cyclic blocks are symmetrical and antisymmetric.

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9

Corr, Brian P., and Cheryl E. Praeger. "Primary cyclic matrices in irreducible matrix subalgebras." Journal of Group Theory 21, no. 4 (July 1, 2018): 667–94. http://dx.doi.org/10.1515/jgth-2018-0012.

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AbstractPrimary cyclic matrices were used (but not named) by Holt and Rees in their version of Parker’s MEAT-AXE algorithm to test irreducibility of finite matrix groups and algebras. They are matrices X with at least one cyclic component in the primary decomposition of the underlying vector space as an X-module. Let {\operatorname{M}(c,q^{b})} be an irreducible subalgebra of {\operatorname{M}(n,q)}, where {n=bc>c}. We prove a generalisation of the Kung–Stong cycle index theorem, and use it to obtain a lower bound for the proportion of primary cyclic matrices in {\operatorname{M}(c,q^{b})}. This extends work of Glasby and the second author on the case {b=1}.

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10

Deveci, Omur, Yesim Akuzum, Erdal Karaduman, and Ozgur Erdag. "The Cyclic Groups via Bezout Matrices." Journal of Mathematics Research 7, no. 2 (March 22, 2015): 34. http://dx.doi.org/10.5539/jmr.v7n2p34.

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<p>In this paper, we define the Bezout matrices by the aid of the characteristic polynomials of the <em>k</em>-step Fibonacci, the generalized order-<em>k</em> Pell and the generalized order-<em>k</em> Jacobsthal sequences then we consider the multiplicative orders of the Bezout matrices when read modulo <em>m</em>. Consequently, we obtain the rules for the order of the cyclic groups by reducing the Bezout matrices modulo <em>m</em>.</p>

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11

MONTGOMERY, AARON M. "Asymptotic Enumeration of Difference Matrices over Cyclic Groups." Combinatorics, Probability and Computing 27, no. 1 (August 1, 2017): 84–109. http://dx.doi.org/10.1017/s0963548317000281.

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We identify a relationship between a certain family of random walks on Euclidean lattices and difference matrices over cyclic groups. We then use the techniques of Fourier analysis to estimate the return probabilities of these random walks, which in turn yields the asymptotic number of difference matrices over cyclic groups as the number of columns increases.

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12

Mahmoodi Rishakani, Akbar, Seyed Mojtaba Dehnavi, Mohmmadreza Mirzaee Shamsabad, and Nasour Bagheri. "Cryptographic properties of cyclic binary matrices." Advances in Mathematics of Communications 15, no. 2 (2021): 311–27. http://dx.doi.org/10.3934/amc.2020068.

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13

Łosiak, Janina, E. Neuman, and Jolanta Nowak. "The inversion of cyclic tridiagonal matrices." Applicationes Mathematicae 20, no. 1 (1988): 93–102. http://dx.doi.org/10.4064/am-20-1-93-102.

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14

Dubeau, F., and J. Savoie. "A remark on cyclic tridiagonal matrices." Applicationes Mathematicae 21, no. 2 (1991): 253–56. http://dx.doi.org/10.4064/am-21-2-253-256.

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15

Li, Zhongshan, Carolyn A. Eschenbach, and Frank J. Hall. "The structure of nonnegative cyclic matrices." Linear and Multilinear Algebra 41, no. 1 (July 1996): 23–33. http://dx.doi.org/10.1080/03081089608818458.

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16

Evans, D. J., and C. Li. "Sor method andp-cyclic matrices (I)." International Journal of Computer Mathematics 36, no. 1-2 (January 1990): 57–76. http://dx.doi.org/10.1080/00207169008803911.

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17

Evans, D. J., and Changjun Li. "Sor method andP-cyclic matrices (II)." International Journal of Computer Mathematics 37, no. 3-4 (January 1990): 239–50. http://dx.doi.org/10.1080/00207169008803952.

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18

McDonald, Judith J., and Pietro Paparella. "Jordan chains of h-cyclic matrices." Linear Algebra and its Applications 498 (June 2016): 145–59. http://dx.doi.org/10.1016/j.laa.2015.02.029.

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19

Karawia, A. A. "Inversion of General Cyclic Heptadiagonal Matrices." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/321032.

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20

Sturmfels, Bernd. "Totally positive matrices and cyclic polytopes." Linear Algebra and its Applications 107 (August 1988): 275–81. http://dx.doi.org/10.1016/0024-3795(88)90250-9.

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21

Audit, Philippe. "Functions of infinite generalized cyclic matrices." Journal of Mathematical Physics 26, no. 3 (March 1985): 361–64. http://dx.doi.org/10.1063/1.526668.

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22

Baldi, Marco, Giovanni Cancellieri, and Franco Chiaraluce. "Iterative Soft-Decision Decoding of Binary Cyclic Codes." Journal of Communications Software and Systems 4, no. 2 (June 22, 2008): 142. http://dx.doi.org/10.24138/jcomss.v4i2.227.

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Binary cyclic codes achieve good error correction performance and allow the implementation of very simpleencoder and decoder circuits. Among them, BCH codesrepresent a very important class of t-error correcting codes, with known structural properties and error correction capability. Decoding of binary cyclic codes is often accomplished through hard-decision decoders, although it is recognized that softdecision decoding algorithms can produce significant coding gain with respect to hard-decision techniques. Several approaches have been proposed to implement iterative soft-decision decoding of binary cyclic codes. We study the technique based on “extended parity-check matrices”, and show that such method is not suitable for high rates or long codes. We propose a new approach, based on “reduced parity-check matrices” and “spread parity-check matrices”, that can achieve better correction performance in many practical cases, without increasing the complexity.

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23

Arizmendi, Octavio, and James A. Mingo. "The cyclic group and the transpose of an R-cyclic matrix." Journal of Operator Theory 85, no. 1 (December 15, 2020): 135–51. http://dx.doi.org/10.7900/jot.2019oct09.2281.

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We show that using the cyclic group the transpose of an R-cyclic matrix can be decomposed along diagonal parts into a sum of parts which are freely independent over diagonal scalar matrices. Moreover, if the R-cyclic matrix is self-adjoint then the off-diagonal parts are R-diagonal.

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24

Zheng, Yanpeng, Sugoog Shon, and Jangyoung Kim. "Cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices." Journal of Mathematical Analysis and Applications 455, no. 1 (November 2017): 727–41. http://dx.doi.org/10.1016/j.jmaa.2017.06.016.

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25

BARBÉ, ANDRÉ M. "FRACTALS BY NUMBERS." Fractals 03, no. 04 (December 1995): 651–61. http://dx.doi.org/10.1142/s0218348x95000588.

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We introduce an extension of an earlier defined simple, number-based matrix substitution system for obtaining fractal matrices, by considering cyclic substitutions. The elements of the resulting matrices are related to representations of their addresses in a mixed number base. The Hutchinson operator for the limit form of a geometrical representation of the fractal matrix is derived. It is shown that the class of fractal limit sets obtainable from cyclic substitutions does not extend the class obtainable from the simple substitutions.

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26

Schell, S. V. "Asymptotic moments of estimated cyclic correlation matrices." IEEE Transactions on Signal Processing 43, no. 1 (1995): 173–80. http://dx.doi.org/10.1109/78.365296.

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27

Chien, Mao-Ting, and Hiroshi Nakazato. "Singular points of cyclic weighted shift matrices." Linear Algebra and its Applications 439, no. 12 (December 2013): 4090–100. http://dx.doi.org/10.1016/j.laa.2013.10.012.

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28

Baker, Charles E., and Boris S. Mityagin. "Localization of eigenvalues of doubly cyclic matrices." Linear Algebra and its Applications 540 (March 2018): 160–202. http://dx.doi.org/10.1016/j.laa.2017.11.016.

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29

Jang, Ji-Woong, Jong-Seon No, and Habong Chung. "Butson Hadamard matrices with partially cyclic core." Designs, Codes and Cryptography 43, no. 2-3 (May 18, 2007): 93–101. http://dx.doi.org/10.1007/s10623-007-9065-6.

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30

Lampio, Pekka H. J., and Patric R. J. Östergård. "Classification of difference matrices over cyclic groups." Journal of Statistical Planning and Inference 141, no. 3 (March 2011): 1194–207. http://dx.doi.org/10.1016/j.jspi.2010.09.023.

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31

Glasby, S. P. "The Meat-axe and f-cyclic matrices." Journal of Algebra 300, no. 1 (June 2006): 77–90. http://dx.doi.org/10.1016/j.jalgebra.2006.01.026.

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32

Lv, Xiao-Guang, and Ting-Zhu Huang. "The Inverses of Block Toeplitz Matrices." Journal of Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/207176.

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We study the inverses of block Toeplitz matrices based on the analysis of the block cyclic displacement. New formulas for the inverses of block Toeplitz matrices are proposed. We show that the inverses of block Toeplitz matrices can be decomposed as a sum of products of block circulant matrices. In the scalar case, the inverse formulas are proved to be numerically forward stable, if the Toeplitz matrix is nonsingular and well conditioned.

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33

Balonin, Nikolay, and Dragomir Dokovic. "Three new lengths for cyclic Legendre pairs." Information and Control Systems, no. 1 (February 25, 2021): 2–7. http://dx.doi.org/10.31799/1684-8853-2021-1-2-7.

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Introduction: It is conjectured that the cyclic Legendre pairs of odd lengths >1 always exist. Such a pair consists of two functions a, b: G→Z, whose values are +1 or −1, and whose periodic autocorrelation function adds up to the constant value −2 (except at the origin). Here G is a finite cyclic group and Z is the ring of integers. These conditions are fundamental and the closely related structure of Hadamard matrices having a two circulant core and double border is incompletely described in literature, which makes its study especially relevant. Purpose: To describe the two-border two-circulant-core construction for Legendre pairs having three new lengths. Results: To construct new Legendre pairs we use the subsets X={x∈G: a(x)=–1} and Y={x∈G: b(x)=–1} of G. There are 20 odd integers v less than 200 for which the existence of Legendre pairs of length v is undecided. The smallest among them is v=77. We have constructed Legendre pairs of lengths 91, 93 and 123 reducing thereby the number of undecided cases to 17. In the last section of the paper we list some new examples of cyclic Legendre pairs for lengths v≤123. Practical relevance: Hadamard matrices are used extensively in the problems of error-free coding, and compression and masking of video information. Programs for search of Hadamard matrices and a library of constructed matrices are used in the mathematical network “mathscinet.ru” together with executable on-line algorithms

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34

Brahmi, Amine, Hicham Ghennioui, Christophe Corbier, François Guillet, and M’hammed Lahbabi. "Blind Separation of Cyclostationary Sources Sharing Common Cyclic Frequencies Using Joint Diagonalization Algorithm." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/2546838.

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We propose a new method for blind source separation of cyclostationary sources, whose cyclic frequencies are unknown and may share one or more common cyclic frequencies. The suggested method exploits the cyclic correlation function of observation signals to compose a set of matrices which has a particular algebraic structure. The aforesaid matrices are automatically selected by proposing two new criteria. Then, they are jointly diagonalized so as to estimate the mixing matrix and retrieve the source signals as a consequence. The nonunitary joint diagonalization (NU-JD) is ensured by Broyden-Fletcher-Goldfarb-Shanno (BFGS) method which is the most commonly used update strategy for implementing a quasi-Newton technique. The efficiency of the method is illustrated by numerical simulations in digital communications context, which show good performances comparing to other state-of-the-art methods.

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35

Gavelia, S. P. "To construction of Green matrices of edge problems of theory of flat hulls with cyclic periodicity." Researches in Mathematics, no. 2 (July 10, 2021): 10. http://dx.doi.org/10.15421/246903.

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36

Devecı˙, Ömür, and Erdal Karaduman. "The cyclic groups via the Pascal matrices and the generalized Pascal matrices." Linear Algebra and its Applications 437, no. 10 (November 2012): 2538–45. http://dx.doi.org/10.1016/j.laa.2012.06.024.

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37

Dessalew, Gashaye, Tesfaye Kebede, Gurju Awgichew, and Assaye Walelign. "Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices." Abstract and Applied Analysis 2021 (May 31, 2021): 1–7. http://dx.doi.org/10.1155/2021/8343207.

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This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.

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38

Kocik, Jerzy. "A Porism Concerning Cyclic Quadrilaterals." Geometry 2013 (August 13, 2013): 1–5. http://dx.doi.org/10.1155/2013/483727.

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We present a geometric theorem on a porism about cyclic quadrilaterals, namely, the existence of an infinite number of cyclic quadrilaterals through four fixed collinear points once one exists. Also, a technique of proving such properties with the use of pseudounitary traceless matrices is presented. A similar property holds for general quadrics as well as for the circle.

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39

KOPELIOVICH, YAACOV. "THETA CONSTANT IDENTITIES AT PERIODS OF COVERINGS OF DEGREE 3." International Journal of Number Theory 04, no. 05 (October 2008): 725–33. http://dx.doi.org/10.1142/s1793042108001663.

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40

Sabri, K., M. El Badaoui, F. Guillet, A. Adib, and D. Aboutajdine. "On Blind MIMO System Identification Based on Second-Order Cyclic Statistics." Research Letters in Signal Processing 2008 (2008): 1–5. http://dx.doi.org/10.1155/2008/539139.

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This letter introduces a new frequency domain approach for either MIMO System Identification or Source Separation of convolutive mixtures in cyclostationary context. We apply the joint diagonalization algorithm to a set of cyclic spectral density matrices of the measurements to identify the mixing system at each frequency up to permutation and phase ambiguity matrices. An efficient algorithm to overcome the frequency dependent permutations and to recover the phase, even for non-minimum-phase channels, based on cyclostationarity is also presented. The new approach exploits the fact that each input has a different and specific cyclic frequency. A comparison with an existing MIMO method is proposed.

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41

Vysotskaya, Viktoriya V., and Lev I. Vysotsky. "Invertible matrices over some quotient rings: identification, generation, and analysis." Discrete Mathematics and Applications 32, no. 4 (August 1, 2022): 263–78. http://dx.doi.org/10.1515/dma-2022-0022.

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Abstract We study matrices over quotient rings modulo univariate polynomials over a two-element field. Lower bounds for the fraction of the invertible matrices among all such matrices of a given size are obtained. An efficient algorithm for calculating the determinant of matrices over these quotient rings and an algorithm for generating random invertible matrices (with uniform distribution on the set of all invertible matrices) are proposed and analyzed. An effective version of the latter algorithm for quotient rings modulo polynomials of form x r − 1 is considered and analyzed. These methods may find practical applications for generating keys of cryptographic schemes based on quasi-cyclic codes such as LEDAcrypt.

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42

TARASOV, VITALY O. "CYCLIC MONODROMY MATRICES FOR THE R-MATRIX OF THE SIX-VERTEX MODEL AND THE CHIRAL POTTS MODEL WITH FIXED SPIN BOUNDARY CONDITIONS." International Journal of Modern Physics A 07, supp01b (April 1992): 963–75. http://dx.doi.org/10.1142/s0217751x92004129.

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Irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model are described. As a consequence, the direct computation of spectra for transfer-matrices of the chiral Potts model with special fixed-spin boundary conditions is done. The generalization of simple Baxter's Hamiltonian is proposed.

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43

A. Zain, Adnan. "On Group Codes Over Elementary Abelian Groups." Sultan Qaboos University Journal for Science [SQUJS] 8, no. 2 (June 1, 2003): 145. http://dx.doi.org/10.24200/squjs.vol8iss2pp145-151.

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For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group. We also lift the theorem that relates the parity check and the generator matrices of linear codes over finite fields to group codes over elementary Abelian groups. Some new codes that are MDS, self-dual, and cyclic over the Abelian group with four elements are given.

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44

Bolotnikov, Vladimir. "Cyclic matrices and polynomial interpolation over division rings." Linear Algebra and its Applications 646 (August 2022): 132–74. http://dx.doi.org/10.1016/j.laa.2022.03.030.

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45

Beasley, Leroy B., and Sang-Gu Lee. "Linear operators strongly preservingr-cyclic matrices over semirings." Linear and Multilinear Algebra 35, no. 3-4 (August 1993): 325–37. http://dx.doi.org/10.1080/03081089308818265.

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46

Chien, Mao-Ting, and Hiroshi Nakazato. "Hyperbolic forms associated with cyclic weighted shift matrices." Linear Algebra and its Applications 439, no. 11 (December 2013): 3541–54. http://dx.doi.org/10.1016/j.laa.2013.09.018.

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47

Neumann, Peter M., and Cheryl E. Praeger. "Cyclic Matrices in Classical Groups over Finite Fields." Journal of Algebra 234, no. 2 (December 2000): 367–418. http://dx.doi.org/10.1006/jabr.2000.8548.

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48

Nica, Alexandru, Dimitri Shlyakhtenko, and Roland Speicher. "R-Cyclic Families of Matrices in Free Probability." Journal of Functional Analysis 188, no. 1 (January 2002): 227–71. http://dx.doi.org/10.1006/jfan.2001.3814.

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49

Kim, Doyoon, Byeongdu Lee, Brittany Marshall, Stavros Thomopoulos, and Young-Shin Jun. "Cyclic strain enhances the early stage mineral nucleation and the modulus of demineralized bone matrix." Biomaterials Science 9, no. 17 (2021): 5907–16. http://dx.doi.org/10.1039/d1bm00884f.

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50

Abuzin, Leonid, Nikolai Unknown, Dragomir Ðoković, and Ilias Kotsireas. "Hadamard matrices from Goethals — Seidel difference families with a repeated block." Information and Control Systems, no. 5 (October 16, 2019): 2–9. http://dx.doi.org/10.31799/1684-8853-2019-5-2-9.

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Purpose: To construct Hadamard matrices by using Goethals — Seidel difference families having a repeated block, generalizingthe so called propus construction. In particular we construct the first examples of symmetric Hadamard matrices of order 236.Methods: The main ingredient of the propus construction is a difference family in a finite abelian group of order v consisting offour blocks (X1, X2, X3, X4) where X1 is symmetric and X2 X3. The parameters (v; k1, k2, k3, k4; λ) of such family must satisfythe additional condition ki  λ  v. We modify this construction by imposing different symmetry conditions on some of theblocks and construct many examples of Hadamard matrices of this kind. In this paper we work with the cyclic group Zv of order v.For larger values of v we build the blocks Xi by using the orbits of a suitable small cyclic subgroup of the automorphism groupof Zv. Results: We continue the systematic search for symmetric Hadamard matrices of order 4v by using the propus construction.Such searches were carried out previously for odd v  51. We extend it to cover the case v53. Moreover we construct thefirst examples of symmetric Hadamard matrices of order 236. A wide collection of symmetric and skew-symmetric Hadamardmatrices was obtained and the corresponding difference families tabulated by using the symmetry properties of their blocks.Practical relevance: Hadamard matrices are used extensively in the problems of error-free coding, compression and masking ofvideo information. Programs for search of symmetric Hadamard matrices and a library of constructed matrices are used in themathematical network Internet together with executable on line algorithms.

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