On the Gröbner bases of some symmetric systems and their application to coding theory.

DOI10.1016/S0747-7171(02)00131-1zbMath1042.13017OpenAlexW2067546693MaRDI QIDQ1426139

Ferdinando Mora, Massimiliano Sala

Publication date: 14 March 2004

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

Full work available at URL: https://doi.org/10.1016/s0747-7171(02)00131-1

zbMATH Keywords

Gröbner basiscyclic codesymmetric functionsminimum distanceaccelerating the computation

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Cyclic codes (94B15)

Related Items (11)

Bases for local Weyl modules for the hyper and truncated current \(\mathfrak{sl}_2\)-algebras ⋮ A combinatorial approach to the Groebner bases for ideals generated by elementary symmetric functions ⋮ The \(K\)-theory of versal flags and cohomological invariants of degree 3 ⋮ Generalizing Tanisaki's ideal via ideals of truncated symmetric functions ⋮ Products of ideals and jet schemes ⋮ Gröbner bases of Hilbert ideals of alternating groups ⋮ Correcting errors and erasures via the syndrome variety ⋮ GRÖBNER BASIS TECHNIQUES TO COMPUTE WEIGHT DISTRIBUTIONS OF SHORTENED CYCLIC CODES ⋮ The power series Dedekind-Mertens number ⋮ A commutative algebra approach to linear codes ⋮ Gröbner bases for the Hilbert ideal and coinvariants of the dihedral groupD_2p

Uses Software

• CoCoA
• Macaulay2

Cites Work

• On the decoding of cyclic codes using Gröbner bases
• Gröbner bases and distance of cyclic codes
• The Chen-Reed-Helleseth-Truong decoding algorithm and the Gianni-Kalkbrenner Gröbner shape theorem
• Appendix: The Magma language
• Use of Grobner bases to decode binary cyclic codes up to the true minimum distance
• The intractability of computing the minimum distance of a code
• Spectra of long primitive binary BCH codes cannot approach the binomial distribution
• The Big Mother of all Dualities: Möller Algorithm
• On the key equation
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