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Quasi-cyclic and generalized quasi-cyclic codes and uniqueness of their generators
Discrete Mathematics, Algorithms and Applications, 2022In this paper, we use a novel approach to describe generator polynomials of quasi-cyclic (QC) and generalized QC (GQC) codes over finite fields. Our study of QC- and GQC-codes will be general and not only restricted to one-generator codes. We prove that generator polynomials of QC-codes and GQC-codes are unique.
Taher Abualrub, Padmapani Seneviratne
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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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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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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].
Tom Verhoeff, H van Tilborg
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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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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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Self-orthogonal quasi-cyclic codes
IEEE Transactions on Information Theory, 1967A new class of linear block codes, called self-orthogonal quasi-cyclic codes, is defined. It is shown that the problem of designing these codes is equivalent to the problem of designing disjoint difference sets. As a result, several classes of optimal and near-optimal codes can be constructed analytically and other codes can be found by a computer ...
Richard L. Townsend +1 more
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On spectral design methods for quasi-cyclic codes
2016 IEEE International Symposium on Information Theory (ISIT), 2016A method is provided for constructing upper triangular square matrices over the univariate polynomial ring over a finite field, under certain constraints on the eigenvalues of the matrices. In some cases of interest, the degree of the determinant of such matrices is shown to be the smallest possible.
Ron M. Roth, Alexander Zeh
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On the Girth of Quasi-Cyclic Protograph LDPC Codes
IEEE Transactions on Information Theory, 2012In this paper, we study the relationships between the girth of the Tanner graph of a quasi cyclic (QC) protograph low-density parity-check (LDPC) code, on one hand, and the lifting degree and the size and the structure of the base graph, on the other hand.
Mehdi Karimi, Amir H. Banihashemi
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