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New classes of quantum codes on closed orientable surfaces

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Abstract

In this paper we construct two classes of binary quantum error-correcting codes on closed orientable surfaces. These codes are derived from self-dual orientable embeddings of complete bipartite graphs and complete multipartite graphs on the corresponding closed orientable surfaces. We also show a table comparing the rate of these quantum codes when fixing the minimum distance to 3 and 4.

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Authors and Affiliations

  1. Department of Computer Engineering, University College of Nabi Akram, No. 1283, Rah Ahan Street, Tabriz, Iran

    Avaz Naghipour

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  1. Avaz Naghipour
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Correspondence to Avaz Naghipour.

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Appendix

Appendix

In this Appendix, we give an object-oriented package in Matlab to compute minimum distance of quantum codes derived from self-dual orientable embeddings of Ks, s for s ≥ 4. After finding the matrices HX and HZ using the method of rotation scheme [15] for constructing orientable embeddings of Ks, s, we can then determine the minimum distance of the associated quantum code. The following algorithm comes from [21].

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Naghipour, A. New classes of quantum codes on closed orientable surfaces. Cryptogr. Commun. 11, 999–1008 (2019). https://doi.org/10.1007/s12095-018-0347-9

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