Asymptotically good 4-quasi transitive algebraic geometry codes over prime fields

TL;DR

This paper investigates the asymptotic properties of 4-quasi transitive algebraic geometry codes over prime fields, demonstrating their goodness through towers of algebraic function fields.

Contribution

It introduces a family of 4-quasi transitive algebraic geometry codes and proves their asymptotic goodness over many prime fields using algebraic function field towers.

Findings

Family of 4-quasi transitive codes is asymptotically good over many prime fields

Utilizes towers of algebraic function fields to establish asymptotic properties

Advances understanding of algebraic geometry codes over prime fields

Abstract

We study the asymptotic behavior of a family of algebraic geometry codes which are 4-quasi transitive linear codes. We prove that this family is asymptotically good over many prime fields using towers of algebraic function fields.