Entanglement-Assisted Quantum Error Correcting Codes From RS Codes and BCH Codes with Extension Degree 2

Abstract

Entanglement-assisted quantum error correcting codes (EAQECCs) constructed from Reed-Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs coming from any Reed-Solomon code, for the Hermitian metric, and from any BCH code with extension degree $2$ and consecutive cyclotomic cosets, for both the Euclidean and the Hermitian metric. The main task in this work is the computation of a completely general formula for $c$, the minimum number of required maximally entangled quantum states.

References in corpus (9)

• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Correcting Quantum Errors with Entanglement
• Catalytic quantum error correction
• Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
• Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators
• On squares of cyclic codes
• Stabilizer quantum codes from $J$-affine variety codes and a new Steane-like enlargement
• Quantum codes from affine variety codes and their subfield-subcodes
• On the distance of stabilizer quantum codes from $J$-affine variety codes