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 $$[[127,63, {\ge }12]]_2$$[[127,63,≥12]]2 and $$[[63,45, {\ge }6]]_4$$[[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.

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