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Two Classes of Quantum MDS Codes with Large Minimal Distance
Published 10 Oct 2024 in cs.IT and math.IT | (2410.17280v1)
Abstract: In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian self-orthogonal, which yields quantum MDS codes by utilizing Hermitian type CSS construction. In some cases, these codes have minimal distances larger than $q/2$. Also, the parameters of these codes have never been reported before.
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