Reed‐muller codes: an ideal theory approach

DOI10.1080/00927879708825862zbMath0868.94045OpenAlexW2009527740MaRDI QIDQ3124345

Horacio Tapia-Recillas, Carlos Rentería Márquez

Publication date: 13 March 1997

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879708825862

zbMATH Keywords

Reed-Muller codesKoszul complexHilbert functioncommutative algebra

Mathematics Subject Classification ID

Related Items (15)

Wedderburn decomposition of finite group algebras. ⋮ Projective nested Cartesian codes ⋮ Minimum distance of some evaluation codes ⋮ Initially regular sequences and depths of ideals ⋮ On low weight codewords of generalized affine and projective Reed-Muller codes ⋮ Lifted projective Reed-Solomon codes ⋮ On the next-to-minimal weight of projective Reed-Muller codes ⋮ The minimum distance of parameterized codes on projective tori ⋮ Affine Cartesian codes ⋮ Towards the complete determination of next-to-minimal weights of projective Reed-Muller codes ⋮ Codes over a weighted torus ⋮ A note on Nullstellensatz over finite fields ⋮ Projective Reed-Muller type codes on higher dimensional scrolls ⋮ Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes ⋮ Reed-Muller-type codes over the Segre variety

Cites Work

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• The parameters of projective Reed-Müller codes
• On graded rings. I
• On the number of rational points on codimension 1 algebraic sets in \(\mathbb{P}^ n (\mathbb{F}_ q)\)
• Cayley-Bacharach Schemes and Their Canonical Modules
• Projective Reed-Muller codes
• Use of Grobner bases to decode binary cyclic codes up to the true minimum distance
• Linear codes associated to the ideal of points in P^dAnd its canonical module
• Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes
• On generalized ReedMuller codes and their relatives

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