On certain self-orthogonal AG codes with applications to Quantum error-correcting codes

TL;DR

This paper presents a new method for constructing quantum error-correcting codes using self-orthogonal algebraic geometry codes derived from special algebraic curves called Swiss curves, expanding previous approaches.

Contribution

It introduces a novel construction of quantum codes from self-orthogonal AG codes based on Swiss curves, extending prior methods and applying to various well-known algebraic curves.

Findings

Constructed quantum codes from Swiss curves with many rational points.

Extended previous quantum code constructions to new classes of algebraic curves.

Demonstrated applications to Castle, GK, and maximal curves.

Abstract

In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss curves. Several classes of well-known algebraic curves with many rational points turn out to be Swiss curves. Examples are given by Castle curves, GK curves, generalized GK curves and the Abdon-Bezerra-Quoos maximal curves. Applications of our method to these curves are provided. Our construction extends a previous one due to Hernando, McGuire, Monserrat, and Moyano-Fernandez.