English

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.

Keywords

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

R2 v1 2026-06-21T20:13:03.085Z