English

Block-transitive algebraic geometry codes attaining the Tsfasman-Vladut-Zink bound

Number Theory 2019-12-04 v2 Combinatorics

Abstract

We study the asymptotic behavior of a family of algebraic geometry codes, which we call block-transitive, that generalizes the classes of transitive and quasi-transitive codes. We prove, by using towers of algebraic function fields, that there are sequences of codes in this family attaining the Tsfasman-Vladut-Zink bound over finite fields of square cardinality. We give the exact length of these codes as well as explicit lower bounds for their parameters.

Keywords

Cite

@article{arxiv.1710.02395,
  title  = {Block-transitive algebraic geometry codes attaining the Tsfasman-Vladut-Zink bound},
  author = {María Chara and Ricardo A. Podestá and Ricardo Toledano},
  journal= {arXiv preprint arXiv:1710.02395},
  year   = {2019}
}

Comments

24 pages. Some typos and errors corrected. Small changes from the 2017's version. arXiv admin note: text overlap with arXiv:1603.03398