1-generator quasi-cyclic codes over finite chain rings

DOI10.1007/s00200-012-0182-8zbMath1326.94136OpenAlexW1976515744MaRDI QIDQ1938504

Yong-Lin Cao

Publication date: 21 February 2013

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-012-0182-8

zbMATH Keywords

Gröbner basisdirect sum decompositionfinite chain ringquasi-cyclic codeparity check polynomial in standard form

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cyclic codes (94B15) Structure of finite commutative rings (13M05)

Related Items (9)

Optimal binary codes and binary construction of quantum codes ⋮ On the ℤ_q-Simplex codes and its weight distribution for dimension 2 ⋮ Unnamed Item ⋮ Self-dual and LCD double circulant codes over a class of non-local rings ⋮ Codes over affine algebras with a finite commutative chain coefficient ring ⋮ Left dihedral codes over Galois rings \(\mathrm{GR}(p^2, m)\) ⋮ A class of 1-generator quasi-cyclic codes over finite chain rings ⋮ On the structure of 1-generator quasi-polycyclic codes over finite chain rings ⋮ Note on quasi-twisted codes and an application

Cites Work

• Unnamed Item
• Generalized quasi-cyclic codes over Galois rings: structural properties and enumeration
• Quaternary 1-generator quasi-cyclic codes
• On the structure of linear and cyclic codes over a finite chain ring
• On the groups of units of finite commutative chain rings.
• Cyclic codes and minimal strong Gröbner bases over a principal ideal ring.
• Strong Gröbner bases for polynomials over a principal ideal ring
• A Class of 1-Generator Quasi-Cyclic Codes
• Gröbner Bases, Coding, and Cryptography
• On the Hamming distance of linear codes over a finite chain ring

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