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Structure and performance of generalized quasi-cyclic codes [PDF]
Finite Fields and Their Applications, 2017 Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of concatenated codes.
Cem Güneri +5 more
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Symplectic Self-Orthogonal Quasi-Cyclic Codes
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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On the additive cyclic structure of quasi-cyclic codes [PDF]
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cem Güneri +2 more
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Construction of Quasi-Cyclic Product Codes
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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Lower Bound on the Minimum Distance of Single-Generator Quasi-Twisted Codes
Mathematics, 2023 We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes.
Adel Alahmadi +2 more
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An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes [PDF]
MATEC Web of Conferences, 2021 In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes.
Yao Yu, Ma Yuena, Li Husheng, Lv Jingjie
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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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CoRR, 2020 arXiv admin note: text overlap with arXiv:1906 ...
Güneri, Cem, Ling, San, Özkaya, Buket
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Quasi-Cyclic LDPC Codes of Column-Weight Two Using a Search Algorithm
EURASIP Journal on Advances in Signal Processing, 2007 This article introduces a search algorithm for constructing quasi-cyclic LDPC codes of column-weight two. To obtain a submatrix structure, rows are divided into groups of equal sizes.
Michael Liebelt, Gabofetswe Malema
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Quasi-Cyclic Codes Via Unfolded Cyclic Codes and Their Reversibility
IEEE Access, 2019 The finite field $\mathbb {F}_{q^\ell }$ of $q^\ell $ elements contains $\mathbb {F}_{q}$ as a subfield. If $\theta \in \mathbb {F}_{q^\ell }$ is of degree $\ell $ over $\mathbb {F}_{q}$ , it can be used to unfold elements of $\mathbb {F}_{q^\
Ramy Taki Eldin, Hajime Matsui
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