Use of Grobner bases to decode binary cyclic codes up to the true minimum distance

DOI10.1109/18.333885zbMath0812.94019OpenAlexW2171613506MaRDI QIDQ4324145

Tor Helleseth, Xuemin Chen, Irving S. Reed, Trieu-Kien Truong

Publication date: 1 March 1995

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/18.333885

zbMATH Keywords

Gröbner basesdecodingcyclic codesideal theoryerror-locator polynomial

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Cyclic codes (94B15) Decoding (94B35)

Related Items (14)

Matrix-product structure of repeated-root cyclic codes over finite fields ⋮ A lookup table decoding of systematic \((47, 24, 11)\) quadratic residue code ⋮ On the decoding of the \((24, 12, 8)\) Golay code ⋮ Towards a Gröbner-free approach to coding ⋮ Unnamed Item ⋮ On the Gröbner bases of some symmetric systems and their application to coding theory. ⋮ Correcting errors and erasures via the syndrome variety ⋮ GRÖBNER BASIS TECHNIQUES TO COMPUTE WEIGHT DISTRIBUTIONS OF SHORTENED CYCLIC CODES ⋮ Improved decoding of affine-variety codes ⋮ On the decoding of binary cyclic codes with the Newton identities ⋮ Bounded distance decoding of linear error-correcting codes with Gröbner bases ⋮ HELP: a sparse error locator polynomial for BCH codes ⋮ Reed‐muller codes: an ideal theory approach ⋮ Degröbnerization: a political manifesto

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