Coding theory package for Macaulay2

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

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this Macaulay2 package we implement a type of object called a LinearCode. 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 implement a type of object called an EvaluationCode, a construction which allows users 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 implement functions for the syndrome decoding algorithm and locally recoverable code construction, which are important tools in applications of linear codes.
Original languageEnglish
Pages (from-to)113-122
Number of pages10
JournalJournal of Software for Algebra and Geometry
Volume11
Issue number1
DOIs
StatePublished - Jan 1 2021

Keywords

  • Cartesian codes
  • Hamming codes
  • evaluation codes
  • linear codes
  • locally recoverable codes

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