• DOI:10.2140/jsag.2021.11.113
• Corpus ID: 220514533

Coding theory package for Macaulay2

@article{Ball2021CodingTP,
  title={Coding theory package for Macaulay2},
  author={Taylor Ball and Eduardo Camps and Henry Chimal-Dzul and Delio Jaramillo-Velez and Hiram H. L'opez and Nathan S. Nichols and Matthew Perkins and Ivan Soprunov and German Vera-Mart'inez and Gwyneth R. Whieldon},
  journal={ArXiv},
  year={2021},
  volume={abs/2007.06795}
}

• Taylor Ball, Eduardo Camps, +7 authors Gwyneth R. Whieldon
• Published 14 July 2020
• Computer Science
• ArXiv

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{this https URL}