On cyclic algebraic-geometry codes

TL;DR

This paper introduces cyclic algebraic geometry codes, exploring their construction via automorphisms of algebraic function fields and analyzing their properties and equivalences.

Contribution

It presents new conditions for constructing cyclic algebraic geometry codes and studies their relation to cyclic extensions and monomial equivalence.

Findings

Cyclic algebraic geometry codes can be constructed using automorphisms of algebraic function fields.

The codes are closely related to cyclic extensions of function fields.

A detailed analysis of monomial equivalence for codes over rational function fields.

Abstract

In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms. We prove that cyclic algebraic geometry codes constructed in this way are closely related to cyclic extensions. We also give a detailed study of the monomial equivalence of cyclic algebraic geometry codes constructed with our method in the case of a rational function field.