Abstract
In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed–Solomon codes over finite fields of odd characteristic. Among our constructions, there are many MDS self-dual codes with new parameters which have never been reported. When q is square of odd prime power, the total number of lengths of MDS self-dual codes over \(\mathbb {F}_q\) presented in this paper is much more than those in all the previous results.
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Acknowledgements
The authors thank the editor and anonymous referees for their suggestions to improve the readability of this paper. This work is partially supported by National Natural Science Foundation of China(NSFC) under Grant 11471008(J.Luo) and Grant 11871025(H.Liu). This work is also supported by the Fundamental Research Funds for the Central Universities (Innovation Funding Project) under Grant 2019CXZZ075(X.Fang) and Grant CCNU18TS028(J.Luo).
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Fang, X., Lebed, K., Liu, H. et al. New MDS self-dual codes over finite fields of odd characteristic. Des. Codes Cryptogr. 88, 1127–1138 (2020). https://doi.org/10.1007/s10623-020-00734-x
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DOI: https://doi.org/10.1007/s10623-020-00734-x