Minimum distance functions of graded ideals and Reed-Muller-type codes

DOI10.1016/j.jpaa.2016.06.006zbMath1352.13016arXiv1512.06868OpenAlexW2963609083MaRDI QIDQ326562

Yuriko Pitones, José Martínez-Bernal, Rafael H. Villarreal

Publication date: 12 October 2016

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.06868

zbMATH Keywords

Gröbner basesHilbert functionCarvalho, Lopez-Neumann and López conjecturegraded idealminimum distance functionReed-Muller-type code

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

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Uses Software

• Macaulay2

Cites Work

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• The Geometry of Syzygies
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• Monomial Algebras
• Reed-Muller codes on complete intersections.

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