Results 11 to 20 of about 848,601 (293)
Quasi-cyclic complementary dual codes [PDF]
Finite Fields and Their Applications, 2016 LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized.
Cem Güneri +2 more
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Design of LDPC Codes: A Survey and New Results [PDF]
Journal of Communications Software and Systems, 2006 This survey paper provides fundamentals in the design of LDPC codes. To provide a target for the code designer, we first summarize the EXIT chart technique for determining(near-)optimal degree distributions for LDPC code ensembles.
Gianluigi Liva +5 more
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Construction of Quasi-Cyclic Product Codes [PDF]
CoRR, 2015 Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gr{ö}bner basis of a quasi-cyclic component code and the generator polynomial of a second cyclic component code, an explicit expression of the basis of the generating set of the quasi-cyclic product code is given.
Alexander Zeh, San Ling
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On quasi-cyclic codes as a generalization of cyclic codes [PDF]
Finite Fields and Their Applications, 2012 In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic codes of length m and ideals of M_l(Fq)[X]/(X^m-1).
Morgan Barbier +2 more
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Symplectic Self-Orthogonal Quasi-Cyclic Codes [PDF]
IEEE Transactions on Information Theory, 2023 This paper was published in IEEE TIT. In this version, we have corrected some minor errors, among which the most significant change is that the constraint $\gcd(\bar{f}_0(x),g(x))=1$ in Theorem 5 has been corrected to $\gcd(f_0(x),g(x))=1$
Chaofeng Guan +3 more
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, 2021 Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some asymptotic results,
Güneri, Cem, Özkaya, Buket, Ling, San
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Quasi-twisted codes as contractions of quasi-cyclic codes [PDF]
, 2023 We consider the quasi-twisted codes as contractions of quasi-cyclic codes and construct a family of q-ary quasi-cyclic codes whose codewords have r-divisible weights, where r | q − 1.
Özbudak, Ferruh +3 more
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Multidimensional Quasi-Cyclic and Convolutional Codes [PDF]
IEEE Transactions on Information Theory, 2016 We introduce multidimensional analogues of quasi-cyclic (QC) codes and study their algebraic structure. We demonstrate a concatenated structure for multidimensional QC codes and use this to prove that this class of codes is asymptotically good. We also relate the new family of codes to convolutional codes.
Cem Güneri, Buket Özkaya
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Reproducible families of codes and cryptographic applications
Journal of Mathematical Cryptology, 2021 Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography.
Santini Paolo +2 more
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Quasi-Cyclic Stern Proof of Knowledge
2022 IEEE International Symposium on Information Theory (ISIT), 2022 The ongoing NIST standardization process has shown that Proof of Knowledge (PoK) based signatures have become an important type of possible post-quantum signatures. Regarding code-based cryptography, the original approach for PoK based signatures is the Stern protocol which allows to prove the knowledge of a small weight vector solving a given instance
Bidoux, Loïc +3 more
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