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

References in corpus (3)

• New Quantum Codes from Evaluation and Matrix-Product Codes
• Feng-Rao decoding of primary codes
• Quantum codes from affine variety codes and their subfield-subcodes

Cited by in corpus (22)

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• Quantum error-correcting codes from Algebraic Geometry codes of Castle type
• On the distance of stabilizer quantum codes from $J$-affine variety codes
• New binary and ternary LCD codes
• Quantum codes from a new construction of self-orthogonal algebraic geometry codes
• Monomial-Cartesian codes and their duals, with applications to LCD codes, quantum codes, and locally recoverable codes
• Improved constructions of nested code pairs
• Entanglement-Assisted Quantum Error Correcting Codes From RS Codes and BCH Codes with Extension Degree 2
• Classical and Quantum Evaluation Codes at the Trace Roots
• An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance
• On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes
• A recursive construction for projective Reed-Muller codes
• Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes
• Locally recoverable $J$-affine variety codes
• Hulls of projective Reed-Muller codes over the projective plane
• On Steane-Enlargement of Quantum Codes from Cartesian Product Point Sets
• Optimal $(r,\delta )$-LRCs from monomial-Cartesian codes and their subfield-subcodes
• Stabilizer quantum codes defined by trace-depending polynomials
• Subfield subcodes of projective Reed-Muller codes
• Steane-Enlargement of Quantum Codes from the Hermitian Curve
• Impure codes exceeding the pure bounds for quantum local recovery
• Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes