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

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.

arXiv comment24 pages. Some typos and errors corrected. Small changes from the 2017's version. arXiv admin note: text overlap with arXiv:1603.03398