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On some binary symplectic self-orthogonal codes

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Abstract

Symplectic self-orthogonal codes over finite fields are an important class of linear codes in coding theory, which can be used to construct quantum codes. In this paper, characterizations of symplectic self-orthogonal codes over finite fields \(F_{q}\) are given. A necessary and sufficient condition for determining symplectic self-orthogonal codes is obtained. Several classes of symplectic self-orthogonal codes are constructed. Furthermore, the symplectic weight distributions of some new classes of binary symplectic self-orthogonal codes are completely determined.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments which help to improve the presentation of this manuscript. 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

    Heqian Xu

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

    Heqian Xu & Wei Du

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  1. Heqian Xu
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  2. Wei Du
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Correspondence to Heqian Xu.

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Xu, H., Du, W. On some binary symplectic self-orthogonal codes. AAECC 33, 321–337 (2022). https://doi.org/10.1007/s00200-020-00455-7

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  • DOI: https://doi.org/10.1007/s00200-020-00455-7

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