On quasi-cyclic codes as a generalization of cyclic codes

DOI10.1016/j.ffa.2012.06.003zbMath1267.94138arXiv1108.3754OpenAlexW2111162716MaRDI QIDQ714456

Christophe Chabot, Guillaume Quintin, Morgan Barbier

Publication date: 11 October 2012

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.3754

zbMATH Keywords

quasi-cyclic codesleft idealsmatrix ringscyclic codesevaluation codeskey equation

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Cyclic codes (94B15) Decoding (94B35)

Related Items (8)

On the girth of Tanner \((3,11)\) quasi-cyclic LDPC codes ⋮ Dual of codes over finite quotients of polynomial rings ⋮ Two-sided Galois duals of multi-twisted codes ⋮ A construction of \(\mathbb{F}_2 \)-linear cyclic, MDS codes ⋮ On BCH split metacyclic codes ⋮ Dihedral codes with prescribed minimum distance ⋮ Half-cyclic, dihedral and half-dihedral codes ⋮ On the locality of quasi-cyclic codes over finite fields

Uses Software

• Magma
• McEliece
• Code Tables

Cites Work

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• Quasi-cyclic codes as codes over rings of matrices
• The Magma algebra system. I: The user language
• Algebraic Cryptanalysis of McEliece Variants with Compact Keys
• Reducing Key Length of the McEliece Cryptosystem
• On the equivalence of McEliece's and Niederreiter's public-key cryptosystems
• On the algebraic structure of quasi-cyclic codes .I. Finite fields
• Good self-dual quasi-cyclic codes exist
• Algebraic structure of quasicyclic codes

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