Stabilizer quantum codes from $J$-affine variety codes and a new Steane-like enlargement

TL;DR

This paper introduces new stabilizer quantum codes with record parameters by generalizing the Steane's enlargement method and using orthogonal subfield-subcodes of $J$-affine variety codes, achieving better performance than existing codes.

Contribution

It presents a novel generalization of Steane's enlargement and constructs new quantum codes from $J$-affine variety codes with improved parameters.

Findings

Quantum codes with parameters $[[127,63, geq 12]]_2$ and $[[63,45, geq 6]]_4$ are achieved.

The codes outperform existing ones in the literature.

New methods for constructing stabilizer codes are introduced.

Abstract

New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters $[[127,63, \geq 12]]_2$ and $[[63,45, \geq 6]]_4$ that are records. These codes are constructed with a new generalization of the Steane's enlargement procedure and by considering orthogonal subfield-subcodes --with respect to the Euclidean and Hermitian inner product-- of a new family of linear codes, the $J$-affine variety codes.