2000 character limit reached
Entanglement-Assisted Quantum Error Correcting Codes From RS Codes and BCH Codes with Extension Degree 2 (2007.01113v2)
Published 2 Jul 2020 in cs.IT and math.IT
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.