MacWilliams extension property for arbitrary weights on linear codes over module alphabets

DOI10.1007/s10623-021-00945-wzbMath1506.94092OpenAlexW3208561693MaRDI QIDQ2109390

Jay A. Wood, Serhii Dyshko

Publication date: 21 December 2022

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-021-00945-w

zbMATH Keywords

linear codeextension theoremcyclic socle

Mathematics Subject Classification ID

Linear codes (general theory) (94B05)

Cites Work

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• MacWilliams extension theorems and the local-global property for codes over Frobenius rings
• Orthogonality matrices for modules over finite Frobenius rings and MacWilliams' equivalence theorem
• A generalized weight for linear codes and a Witt-MacWilliams theorems
• A metric for codes over residue class rings
• Finite-ring combinatorics and MacWilliams' equivalence theorem
• Geometric approach to the MacWilliams extension theorem for codes over module alphabets
• On the equivalence of codes over finite rings
• Characters and the equivalence of codes
• Characteristics of invariant weights related to code equivalence over rings
• Two approaches to the extension problem for arbitrary weights over finite module alphabets
• The extension theorem for Lee and Euclidean weight codes over integer residue rings
• MacWilliams' extension theorem for bi-invariant weights over finite principal ideal rings
• On the equivalence of codes over rings and modules
• The Extension Theorem with Respect to Symmetrized Weight Compositions
• FOUNDATIONS OF LINEAR CODES DEFINED OVER FINITE MODULES: THE EXTENSION THEOREM AND THE MACWILLIAMS IDENTITIES
• Witt's Extension Theorem for mod Four Valued Quadratic Forms
• An elementary proof of the MacWilliams theorem on equivalence of codes
• Duality for modules over finite rings and applications to coding theory
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• FINITE QUASI-FROBENIUS MODULES AND LINEAR CODES
• The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules
• Code equivalence characterizes finite Frobenius rings
• When the extension property does not hold

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