On the equivalence of codes over rings and modules

DOI10.1016/j.ffa.2004.01.001zbMath1082.94020OpenAlexW2109684601MaRDI QIDQ2566957

Hai Quang Dinh, Sergio R. López-Permouth

Publication date: 29 September 2005

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2004.01.001

zbMATH Keywords

codes over finite ringsfinite Frobenius ringsequivalence of codesMacWilliams ringcodes over finite modules

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Other types of codes (94B60)

Related Items (19)

The Extension Theorem with Respect to Symmetrized Weight Compositions ⋮ Group algebras and coding theory ⋮ Geometric approach to the MacWilliams extension theorem for codes over module alphabets ⋮ Frobenius-Artin algebras and infinite linear codes ⋮ Self-dual codes over commutative Frobenius rings ⋮ Feedback equivalence of convolutional codes over finite rings ⋮ MacWilliams extension theorems and the local-global property for codes over Frobenius rings ⋮ Weight-preserving isomorphisms between spaces of continuous functions: the scalar case ⋮ Isometry groups of combinatorial codes ⋮ MacWilliams’ extension theorem for infinite rings ⋮ MacWilliams extension theorem for MDS codes over a vector space alphabet ⋮ Representation of group isomorphisms: the compact case ⋮ When the extension property does not hold ⋮ Code equivalence characterizes finite Frobenius rings ⋮ State space realizations and monomial equivalence for convolutional codes ⋮ Isometry groups of combinatorial codes ⋮ MacWilliams extension property for arbitrary weights on linear codes over module alphabets ⋮ On infinite MacWilliams rings and minimal injectivity conditions ⋮ On extendability of additive code isometries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite-ring combinatorics and MacWilliams' equivalence theorem
• Characters and the equivalence of codes
• Kerdock code in a cyclic form
• An elementary proof of the MacWilliams theorem on equivalence of codes
• Duality for modules over finite rings and applications to coding theory
• A linear construction for certain Kerdock and Preparata codes
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• WHEN SELF-INJECTIVE RINGS ARE QF: A REPORT ON A PROBLEM
• FINITE QUASI-FROBENIUS MODULES AND LINEAR CODES
• Characterization of finite Frobenius rings

This page was built for publication: On the equivalence of codes over rings and modules