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Quantum Information and Computation

Hermitian dual containing BCH codes and construction of new quantum codes

LiRuihu, ZuoFei, LiuYang, XuZongben

Published Jan 1, 2013• 0 citations
Publisher

Abstract

Let q ≥ 3 be a prime power. Maximal designed distances of primitive Hermitian dual containing q2-ary BCH codes (narrow-sense or non-narrow-sense) are determined by a careful analysis of properties ...
DOI
10.5555/2481591.2481594

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Let q≥3q\geq 3q≥3 be a prime power. Maximal designed distances of primitive Hermitian dual containing q2q^{2}q2-ary BCH codes (narrow-sense or non-narrow-sense) are determined by a careful analysis of properties of cyclotomic cosets. Non-narrow-sense BCH codes which achieve these maximal designed distances are presented, and a sequence of nested non-narrow-sense BCH codes that contain these BCH codes with maximal designed distances are constructed and their parameters are computed. Consequently, new nonbinary quantum BCH codes are derived from these non-narrow-sense BCH codes. The nonbinary quantum BCH codes presented here have better parameters than those quantum BCH codes available in the literature.
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