Quantum codes from affine variety codes and their subfield-subcodes

Abstract

We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum Gilbert-Varshamov bound given by Feng and Ma.

Cited by in corpus (16)

• New Quantum Codes from Evaluation and Matrix-Product Codes
• Stabilizer quantum codes from $J$-affine variety codes and a new Steane-like enlargement
• Asymmetric entanglement-assisted quantum error-correcting codes and BCH codes
• 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
• 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
• On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes
• Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes
• A recursive construction for projective Reed-Muller codes
• Locally recoverable $J$-affine variety codes
• Subfield subcodes of projective Reed-Muller codes
• Optimal $(r,\delta )$-LRCs from monomial-Cartesian codes and their subfield-subcodes
• New quantum codes from homothetic-BCH codes