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On the Construction of Nonbinary Quantum BCH Codes

Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. The first two ones are based on Calderbank-Shor-Steane (CSS) construction derived from two nonprimitive BCH codes, not necessarily self-orthogonal. The third one is based on nonbinary Steane's enlargement of CSS codes applied to suitable sub-families of nonprimitive non-narrow-sense BCH codes. The fourth construction is derived from suitable sub-families of Hermitian self-orthogonal nonprimitive non-narrow-sense BCH codes. These constructions generate new families of quantum BCH codes whose parameters are better than the ones available in the literature.

preprint2013arXivOpen access
Giuliano G. La Guardia
math.ITInformation Theoryquant-ph
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Giuliano G. La Guardia

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