Coding theory package for Macaulay2
Abstract
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, ReedSolomon codes, ReedMuller codes, Cartesian codes, monomialCartesian 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/Workshop2020Cleveland/tree/CodingTheory/CodingTheory}
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.06795
 Bibcode:
 2020arXiv200706795B
 Keywords:

 Computer Science  Information Theory;
 94B05;
 13P25;
 14G50;
 11T71
 EPrint:
 J. Softw. Alg. Geom. 11 (2021) 113122