Affine cartesian codes
Commutative Algebra
2024-02-07 v3 Information Theory
Algebraic Geometry
Combinatorics
math.IT
Abstract
We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus, with prescribed parameters. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.
Cite
@article{arxiv.1202.0085,
title = {Affine cartesian codes},
author = {Hiram H. Lopez and Carlos Renteria and Rafael H. Villarreal},
journal= {arXiv preprint arXiv:1202.0085},
year = {2024}
}
Comments
Designs, Codes and Cryptography, to appear