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International Conference on Computer Science and Information Processing

A class of imprimitive BCH codes and new quantum codes

Yang Liu, Yuena Ma, Ruihu Li, Youqian Feng

Published Aug 1, 2012• 0 citations
Publisher

Abstract

Let q be a prime power, l ≥ 2 be even, n=(q-1)(qil-1)/(qi-1). We give necessary and sufficient conditions on dual containing q-ary narrow-sense BCH codes of lengthn, and improve previous upper bound on necessary condition. We present a family of dual containing non-narrow-sense BCH codes of lengthnincluding the BCH code with maximal designed distance, calculate their dimensions and use them to construct new quantum codes, which are better than those constructed from narrow-sense BCH codes.

DOI
10.1109/csip.2012.6308834

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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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