# 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}
}
• 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…
3 Citations
Multivariate Goppa codes
• Computer Science
ArXiv
• 2021
The multivariate Goppa codes are utilized to obtain entanglement-assisted quantum error-correcting codes and to build families of long LCD, self-dual, or self-orthogonal codes.
The dual of an evaluation code
• Mathematics, Computer Science
Des. Codes Cryptogr.
• 2021
This work shows that the dual of an evaluation code is the evaluation code of the algebraic dual, and provides an explicit duality criterion in terms of the vnumber and the Hilbert function of a vanishing ideal for Reed–Muller-type codes corresponding to Gorenstein ideals.
Relative generalized Hamming weights of evaluation codes
• Computer Science
São Paulo Journal of Mathematical Sciences
• 2022
The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes in terms of a footprint bound and it is proved that this bound can be sharp.

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