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New Quantum MDS Codes over Finite Fields (1904.12441v3)
Published 29 Apr 2019 in cs.IT and math.IT
Abstract: In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes can be bigger than $\frac{q}{2}+1$. Comparing to previous known constructions, the lengths of codes in our constructions are more flexible.
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