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International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)

Asymmetric Quantum Codes of Large Z - Distance Constructed from a Class of Quaternary Imprimitive BCH Codes

Ruihu Li, Genqi Xu, Qiang Fu, Fei Zuo

Published Sep 1, 2015• 0 citations
Publisher

Abstract

In this paper, we focus on construction of asymmetric quantum error-correcting codes (AQECCs) from quaternary narrow-sense BCH codes of code length n = 4m-1/3(m≥3 is an integer) via Calderbank-Shor-Steane construction. By a careful analysis on properties of cyclotomic cosets in the defining sets of two ingredient BCH codes B(n, δ1)4and B(n,δ2)4that satisfies B⊥h(n,δ1)4⊆ B(n,δ2)4used for constructing AQECCs, we derive new families of AQECCs with dz> δmaxs+ 1, and thus we can eliminate the unreasonable restriction dz≤ δmaxdevised in previous literature and obtain new AQECCs with greater asymmetry compared with the known results. Here δmaxsis the maximal designed distance of Hermitian dual-containing narrow-sense BCH codes of length n = 4m-1/3.

DOI
10.1109/imccc.2015.121

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On the basis of concepts of skew symmetric-cyclotomic coset and skew asymmetric coset pair,and their properties deeply studied,and methods determined,a maximal design distance of BCH codes with length contained in its Hermitian dual is studied.Thus,such an unsolved problem for maximal design distance of BCH codes with length is solved,upper bound of maximal design distance of BCH codes previously known is improved,and a new upper bound picked up is sharp.By utilizing these Hermitian dual containing non-narrow-sense BCH codes,many new quantum codes with good parameters are constructed,these new quantum codes are better than that constructed from narrow-sense BCH codes in the literature.
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