Abstract
Let \({\mathbb{F}_q}\) be a finite field with order q and D2n be the dihedral group with 2n elements, and gcd(q, 2n) = 1. In this article, the authors give precise descriptions and enumerations of linear complementary dual (LCD) codes and self-orthogonal codes in the finite dihedral group algebras \({\mathbb{F}_q}[{D_{2n}}]\). Some numerical examples are also presented to illustrate the main results.
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The authors are very grateful to the reviewers and the editor for their valuable comments and suggestions to improve the quality of this paper.
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This work was supported by the National Natural Science Foundation of China (Nos. 61772015, 11971321, 12101326), Foundation of Nanjing Institute of Technology (No. CKJB202007), the NUPTSF (No. NY220137), the Guangxi Natural Science Foundation (No. 2020GXNSFAA159053), the National Key Research and Development Program of China (No. 2018YFA0704703), Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-010), the Open Project of Shanghai Key Laboratory of Trustworthy Computing (No. OP202101).
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Gao, Y., Yue, Q. & Wu, Y. LCD Codes and Self-orthogonal Codes in Finite Dihedral Group Algebras. Chin. Ann. Math. Ser. B 42, 791–800 (2021). https://doi.org/10.1007/s11401-021-0291-4
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DOI: https://doi.org/10.1007/s11401-021-0291-4