English

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