Quantum Information and Computation

New families of asymmetric quantum BCH codes

Giuliano G. La Guardia

Published Mar 1, 2011• 24 citations

Abstract

Several families of nonbinary asymmetric quantum Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. These quantum codes have parameters better than the ones available in the literature. Additionally, such codes can be applied in quantum systems where the asymmetry between qudit-flip and phase-shift errors is large.

DOI: 10.26421/qic11.3-4-4

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Quantum Information and Computation

New families of asymmetric quantum BCH codes

Giuliano G. La Guardia

Published Mar 1, 2011• 24 citations

Publisher

Abstract

DOI: 10.26421/qic11.3-4-4

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Three code constructions generating new families of good nonbinary quantum codes are presented in this paper. The first two ones are derived from Hermitian self-orthogonal non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes. The third one is derived from $q$ -ary ($q\ensuremath{\ne}2$ is a prime power) Steane's enlargement of Calderbank-Shor-Steane codes applied to Euclidean self-orthogonal non-narrow-sense BCH codes. The quantum nonbinary BCH codes presented here have parameters better than the ones available in the literature.Three code constructions generating new families of good nonbinary quantum codes are presented in this paper. The first two ones are derived from Hermitian self-orthogonal non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes. The third one is derived from $q$-ary ($q\ensuremath{\ne}2$ is a prime power) Steane's enlargement of Calderbank-Shor-Steane codes applied to Euclidean self-orthogonal non-narrow-sense BCH codes. The quantum nonbinary BCH codes presented here have parameters better than the ones available in the literature.

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q

-ary ($q\ensuremath{\ne}2$ is a prime power) Steane's enlargement of Calderbank-Shor-Steane codes applied to Euclidean self-orthogonal non-narrow-sense BCH codes. The quantum nonbinary BCH codes presented here have parameters better than the ones available in the literature.

Maximal designed distances for nonbinary narrow-sense quantum Bose-Chaudhuri-Hocquenghem (BCH) codes of length

n=\frac{q^4-1}{r}

and new constructions for them are given, where q is an odd prime power. These constructions are capable of designing quantum BCH codes with new parameters. Furthermore, some codes obtained here have better parameters than those constructed by other known constructions.