Gröbner Bases over Commutative Rings and Applications to Coding Theory

DOI10.1007/978-3-540-93806-4_14zbMath1179.13019OpenAlexW2211295369MaRDI QIDQ3652821

Eimear Byrne, Ferdinando Mora

Publication date: 16 December 2009

Published in: Gröbner Bases, Coding, and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-93806-4_14

zbMATH Keywords

Gröbner basesalternant codesGalois ringBerlekamp-Massey algorithmBuchberger's algorithmcommutative ringsdecoding algorithmslist decodingfinite chain ringsFGLM algorithmkey-equationsolution moduleSzekeres-like bases

Mathematics Subject Classification ID

Cryptography (94A60) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Decoding (94B35)

Related Items (6)

Standard bases in mixed power series and polynomial rings over rings ⋮ Algebraic decoding of negacyclic codes over \({\mathbb Z_4}\) ⋮ Lattice of ideals of the polynomial ring over a commutative chain ring ⋮ Buchberger-Zacharias theory of multivariate Ore extensions ⋮ Zacharias representation of effective associative rings ⋮ A primer on ideal theoretical operation in non-commutative polynomial rings

Uses Software

• FGb

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