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On complementary-dual quasi-cyclic codes
Finite Fields and Their Applications, 2009 A linear code with a complementary dual (an LCD code) is a linear code \(C\) whose dual \(C^ \perp\) satisfies \(C\cap C^ \perp= \{0\}\). Necessary and sufficient conditions for a cyclic code be an LCD code were given by \textit{X. Yang} and \textit{J. L. Massey} [Discrete Math. 126, No. 1--3, 391--393 (1994; Zbl 0790.94022)].
M Esmaeili
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Some new binary, quasi-cyclic codes
IEEE Transactions on Information Theory, 1998 By means of local search techniques, five quasi-cyclic codes have been found that have a higher minimum distance than known binary linear codes. The new codes have parameters [102,17,37], [60,20,17], [84,21,27], [105,21,36], and [100,25,30].
H Van Tilborg, Tom Verhoeff
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1-Generator Quasi-Cyclic Codes
Journal of Systems Science and Complexity, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junying Pei, Xuejun Zhang
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Quasi-cyclic codes as codes over rings of matrices
Finite Fields and Their Applications, 2010 International audienceQuasi cyclic codes over a nite eld are viewed as cyclic codes over a non commutative ring of matrices over a nite eld. This point of view permits to generalize some known results about linear recurring sequences and to propose a new
Pierre-Louis Cayrel
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Binary Quasi-Cyclic Goppa Codes
Designs, Codes and Cryptography, 2000A class of quasi-cycic Goppa codes containing irreducibles codes, and partially split ones, is defined. A necessary and sufficient condition for a Goppa code to be quasi-cyclic is given. One more sufficient condition is derived on the defining polynomial of the Goppa code.
Grégoire Bommier, Francis Blanchet
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Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), 2002
Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes.
P. Heijnen, H. van Tilborg, S. Weijs
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Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes.
P. Heijnen, H. van Tilborg, S. Weijs
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IEEE Communications Letters, 2018
Low-density parity-check (LDPC) codes based on affine permutation matrices, APM-LDPC codes, have been attracted recently, because of some advantages rather than QC-LDPC codes in minimum-distance, cycle distribution and error-rate performance. In this letter, circulant and anti-circulant permutation matrices are used to define a class of LDPC codes ...
Zahra Gholami, Mohammad Gholami
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Low-density parity-check (LDPC) codes based on affine permutation matrices, APM-LDPC codes, have been attracted recently, because of some advantages rather than QC-LDPC codes in minimum-distance, cycle distribution and error-rate performance. In this letter, circulant and anti-circulant permutation matrices are used to define a class of LDPC codes ...
Zahra Gholami, Mohammad Gholami
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One-generator quasi-cyclic codes and their dual codes
Discrete Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kanat Abdukhalikov +2 more
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Optimal ternary quasi-cyclic codes
Designs, Codes and Cryptography, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Phil P. Greenough, Ray Hill
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A SPECIAL CLASS OF QUASI-CYCLIC CODES
Bulletin of the Australian Mathematical Society, 2017We study a special class of quasi-cyclic codes, obtained from a cyclic code over an extension field of the alphabet field by taking its image on a basis. When the basis is equal to its dual, the dual code admits the same construction. We give some examples of self-dual codes and LCD codes obtained in this way.
Shi, Minjia +4 more
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