We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.2010 Mathematics Subject Classification. 81P70; 94B65; 94B05.

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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.

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