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

07/02/2020

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by   Carlos Galindo, et al.

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Entanglement-assisted quantum error correcting codes (EAQECCs) from Reed-Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of an EAQECC 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.