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

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, >= 12]]_2 and [[63,45, >= 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.