On the equivalence of codes over finite rings
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Publication:1885353
DOI10.1007/s00200-004-0149-5zbMath1055.94030OpenAlexW1985246216MaRDI QIDQ1885353
Hai Quang Dinh, Sergio R. López-Permouth
Publication date: 28 October 2004
Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00200-004-0149-5
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Finite rings and finite-dimensional associative algebras (16P10) Linear codes (general theory) (94B05) Quasi-Frobenius rings (16L60)
Related Items (13)
Group algebras and coding theory ⋮ Geometric approach to the MacWilliams extension theorem for codes over module alphabets ⋮ Construction of cyclic DNA codes over the ring \(\mathbb{Z}_4 [u / \langle u^2 - 1 \rangle\) based on the deletion distance] ⋮ Frobenius-Artin algebras and infinite linear codes ⋮ Self-dual codes over commutative Frobenius rings ⋮ MacWilliams’ extension theorem for infinite rings ⋮ MacWilliams extension theorem for MDS codes over a vector space alphabet ⋮ When the extension property does not hold ⋮ Code equivalence characterizes finite Frobenius rings ⋮ The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules ⋮ Extension theorems for various weight functions over Frobenius bimodules ⋮ MacWilliams extension property for arbitrary weights on linear codes over module alphabets ⋮ On infinite MacWilliams rings and minimal injectivity conditions
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