# 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} }

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 ScienceArXiv
- 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 ScienceDes. 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 ScienceSão 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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