On the distance of stabilizer quantum codes from $J$-affine variety codes

TL;DR

This paper develops methods to derive quantum stabilizer codes with guaranteed minimum distances from $J$-affine variety codes, leading to new codes with improved parameters or larger distances.

Contribution

It introduces a way to determine the minimum distance of quantum codes from $J$-affine variety codes and their subfield-subcodes, enhancing code construction techniques.

Findings

Derived quantum codes with designed minimum distances.

Produced new quantum codes with better parameters.

Achieved codes with larger distances than previous ones.

Abstract

Self-orthogonal $J$-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the minimum distance was given. In this work, we show how to derive quantum stabilizer codes with designed minimum distance from $J$-affine variety codes and their subfield-subcodes. Moreover, this allows us to obtain new quantum codes, some of them either, with better parameters, or with larger distances than the previously known codes.