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

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