Coding theory package for Macaulay2

DOI10.2140/jsag.2021.11.113zbMath1485.13057arXiv2007.06795OpenAlexW4214485061MaRDI QIDQ2138423

Gwyn Whieldon, German Vera-Martínez, Henry Chimal-Dzul, Eduardo Camps, Matthew Perkins, Delio Jaramillo-Velez, Nathan Nichols, Ivan Soprunov, Taylor Ball, Hiram H. López-Valdez

Publication date: 12 May 2022

Published in: The Journal of Software for Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.06795

zbMATH Keywords

linear codesevaluation codesHamming codeslocally recoverable codesCartesian codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Software, source code, etc. for problems pertaining to commutative algebra (13-04) 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)

Related Items

EvaluationCode ⋮ LinearCode ⋮ CodingTheory.m2

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• A Mathematical Theory of Communication
• Minimum distance functions of graded ideals and Reed-Muller-type codes
• Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
• Cayley-Bacharach and evaluation codes on complete intersections
• Toric complete intersection codes
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• Projective nested Cartesian codes
• Affine Cartesian codes
• On the parameters of \(r\)-dimensional toric codes
• A Family of Optimal Locally Recoverable Codes
• The intractability of computing the minimum distance of a code
• Fundamentals of Error-Correcting Codes
• Minimum distance functions of complete intersections
• Toric Surface Codes and Minkowski Length of Polygons
• Toric Surface Codes and Minkowski Sums