On the algebraic structure of \((M, \sigma, \delta)\)-skew codes

DOI10.1016/j.jalgebra.2023.09.014MaRDI QIDQ6085510

Hassan Ou-azzou, El Mahdi Mouloua, Mustapha Najmeddine, Nuh Aydin

Publication date: 8 November 2023

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

skew polynomial ringpseudo-linear transformationsskew \((\sigma \delta)\)-cyclic codes

Mathematics Subject Classification ID

Theory of error-correcting codes and error-detecting codes (94Bxx) Computational aspects of associative rings (16Zxx) Associative rings and algebras arising under various constructions (16Sxx)

Cites Work

• \((\sigma, \delta)\)-codes
• Coding with skew polynomial rings
• Generalized quasi-cyclic codes: Structural properties and code construction
• Skew-cyclic codes
• Pseudo linear transformations and evaluation in Ore extensions
• Polycyclic codes as invariant subspaces
• Some new linear codes from skew cyclic codes and computer algebra challenges
• \(( \sigma, \delta )\)-skew quasi-cyclic codes over the ring \(\mathbb{Z}_4+u\mathbb{Z}_4 \)
• \((\theta, \delta_\theta)\)-cyclic codes over \(\mathbb{F}_q[u,v / \langle u^2-u, v^2-v, uv-vu \rangle\)]
• \((f, \sigma, \delta)\)-skew polycyclic codes and their applications to quantum codes
• Dual codes of product semi-linear codes
• Dual generalizations of the concept of cyclicity of codes
• Monomial codes seen as invariant subspaces
• Some properties of skew codes over finite fields
• Linear codes using skew polynomials with automorphisms and derivations
• The algebraic structure of codes invariant under a permutation
• Fundamentals of Error-Correcting Codes
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