Gröbner bases over Galois rings with an application to decoding alternant codes

DOI10.1006/jsco.2001.0442zbMath1030.94047OpenAlexW2022466783MaRDI QIDQ5938546

Patrick Fitzpatrick, Eimear Byrne

Publication date: 22 July 2001

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.2001.0442

zbMATH Keywords

Gröbner basesdecodingalternant codescodes over finite rings

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Other types of codes (94B60)

Related Items (12)

A Gröbner basis algorithm for ideals over zero-dimensional valuation rings ⋮ Dynamical Gröbner bases ⋮ On structure and distances of some classes of repeated-root constacyclic codes over Galois rings ⋮ The discrete multidimensional MPUM ⋮ Minimal Gröbner bases and the predictable leading monomial property ⋮ On cyclic codes over Galois rings ⋮ Generalized affine transformation monoids on Galois rings. ⋮ An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings ⋮ Cyclic and negacyclic codes over the Galois ring \(\text{GR}(p^2,m)\) ⋮ Cyclic Codes over Galois Rings ⋮ APPLYING BUCHBERGER'S CRITERIA FOR COMPUTING GRÖBNER BASES OVER FINITE-CHAIN RINGS ⋮ Cyclic codes and minimal strong Gröbner bases over a principal ideal ring.

Cites Work

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• On the decoding of Reed-Solomon and BCH codes over integer residue rings
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