TY - JOUR
T1 - Coding theory package for Macaulay2
AU - Ball, Taylor
AU - Camps, Eduardo
AU - Chimal-Dzul, Henry
AU - Jaramillo-Velez, Delio
AU - López, Hiram
AU - Nichols, Nathan
AU - Perkins, Matthew
AU - Soprunov, Ivan
AU - Vera-Martínez, German
AU - Whieldon, Gwyn
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
KW - Cartesian codes
KW - Hamming codes
KW - evaluation codes
KW - linear codes
KW - locally recoverable codes
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85134670649&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85134670649&origin=inward
U2 - 10.2140/jsag.2021.11.113
DO - 10.2140/jsag.2021.11.113
M3 - Article
SN - 1948-7916
VL - 11
SP - 113
EP - 122
JO - Journal of Software for Algebra and Geometry
JF - Journal of Software for Algebra and Geometry
IS - 1
ER -