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Constructions of Symplectic LCD MDS Codes

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Abstract

Linear complementary dual (LCD) codes are linear codes whose intersections with their duals are trivial. In this paper, characterizations of LCD codes with respect to the symplectic inner product, i.e. symplectic LCD codes, over finite fields are given. Some methods for constructing symplectic LCD codes and symplectic LCD MDS codes are presented. As an application, a class of symplectic LCD MDS codes is constructed by employing Vandermonde matrices, and the corresponding MDS maximal entanglement entanglement-assisted quantum error-correcting codes (EAQECCs) are constructed.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant(61572168) and the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (CN)(gxyqZD2016228).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230027, China

    H. Q. Xu

  2. School of Mathematics and Statistics, Hefei Normal University, Hefei, 230601, China

    H. Q. Xu & W. Du

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  1. H. Q. Xu
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  2. W. Du
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Correspondence to H. Q. Xu.

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Communicated by Miin Huey Ang.

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Xu, H.Q., Du, W. Constructions of Symplectic LCD MDS Codes. Bull. Malays. Math. Sci. Soc. 44, 3377–3390 (2021). https://doi.org/10.1007/s40840-021-01114-x

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  • DOI: https://doi.org/10.1007/s40840-021-01114-x

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