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Asymmetric quantum codes: new codes from old

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An Erratum to this article was published on 10 April 2013

Abstract

In this paper we extend to asymmetric quantum error-correcting codes the construction methods, namely: puncturing, extending, expanding, direct sum and the \(({ \mathbf u}| \mathbf{u}+{ \mathbf v})\) construction. By applying these methods, several families of asymmetric quantum codes can be constructed. Consequently, as an example of application of quantum code expansion developed here, new families of asymmetric quantum codes derived from generalized Reed-Muller codes, quadratic residue, Bose-Chaudhuri-Hocquenghem, character codes and affine-invariant codes are constructed.

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Acknowledgments

I am indebted to the anonymous referee for their valuable comments and suggestions that improve significantly the quality of this paper. Additionally, he/she pointed out that the construction methods presented in the first version of this manuscript (asymmetric quantum codes derived from linear codes) also hold for a more general setting (asymmetric quantum codes derived from additive codes). Based on this suggestion, I have added more results concerning asymmetric codes derived from additive codes. This work was partially supported by the Brazilian Agencies CAPES and CNPq.

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  1. Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, 84030-900 , PR, Brazil

    Giuliano G. La Guardia

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  1. Giuliano G. La Guardia
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Correspondence to Giuliano G. La Guardia.

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La Guardia, G.G. Asymmetric quantum codes: new codes from old. Quantum Inf Process 12, 2771–2790 (2013). https://doi.org/10.1007/s11128-013-0562-4

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