On the distance of stabilizer quantum codes from $J$-affine variety codes

Abstract

Self-orthogonal $J$-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the minimum distance was given. In this work, we show how to derive quantum stabilizer codes with designed minimum distance from $J$-affine variety codes and their subfield-subcodes. Moreover, this allows us to obtain new quantum codes, some of them either, with better parameters, or with larger distances than the previously known codes.

References in corpus (4)

• New Quantum Codes from Evaluation and Matrix-Product Codes
• Stabilizer quantum codes from $J$-affine variety codes and a new Steane-like enlargement
• Feng-Rao decoding of primary codes
• Quantum codes from affine variety codes and their subfield-subcodes

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• Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes
• Classical and Quantum Evaluation Codes at the Trace Roots
• Locally recoverable $J$-affine variety codes
• Quantum $(r,\delta )$-locally recoverable codes
• Subfield subcodes of projective Reed-Muller codes
• Optimal $(r,\delta )$-LRCs from monomial-Cartesian codes and their subfield-subcodes
• Stabilizer quantum codes defined by trace-depending polynomials
• MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes
• Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes
• New quantum codes from homothetic-BCH codes