Coding theory package for Macaulay2

• Published in: arXiv.org 2020-07
• Main Authors: Ball, Taylor, Camps, Eduardo, Henry Chimal-Dzul, Jaramillo-Velez, Delio, López, Hiram H, Nichols, Nathan, Perkins, Matthew, Soprunov, Ivan, Vera-Martínez, German, Whieldon, Gwyn
• Format: Article
• Language: English
• Subjects: Algorithms; Binary system; Cartesian coordinates; Codes; Decoding; Hamming codes; Linear codes; Mathematical analysis; Matrix methods
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2007.06795

In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code, length, dimension, and minimum distance, among others. We define an object {\it evaluation code}, a construction which allows to study linear codes using tools of algebraic geometry and commutative algebra. We implement functions to generate important families of linear codes such as Hamming codes, cyclic codes, Reed--Solomon codes, Reed--Muller codes, Cartesian codes, monomial--Cartesian codes, and toric codes. In addition, we define functions for the syndrome decoding algorithm and locally recoverable code construction, which are important tools in applications of linear codes. The package \textit{CodingTheory.m2} is available at \url{https://github.com/Macaulay2/Workshop-2020-Cleveland/tree/CodingTheory/CodingTheory}