Evaluation codes and their basic parameters
Commutative Algebra
2020-05-20 v5 Information Theory
Algebraic Geometry
Combinatorics
math.IT
Number Theory
Abstract
The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of Reed--Muller-type codes, and we determine the minimum distance of toric codes over hypersimplices, and the 1st and 2nd generalized Hamming weights of squarefree evaluation codes.
Keywords
Cite
@article{arxiv.1907.13217,
title = {Evaluation codes and their basic parameters},
author = {Delio Jaramillo and Maria Vaz Pinto and Rafael H. Villarreal},
journal= {arXiv preprint arXiv:1907.13217},
year = {2020}
}
Comments
We thank Nupur Patanker for pointing out an error in Proposition 2.5. This proposition has been deleted