Abstract
A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider new constructions of MDS self-dual codes via generalized Reed-Solomon (GRS) codes and their extended codes. The critical idea of our constructions is to choose suitable evaluation points such that the corresponding (extended) GRS codes are self-dual. The evaluation set of our constructions consists of a subgroup of finite fields and its cosets in a bigger subgroup. Four new families of MDS self-dual codes are then obtained. Moreover, by the Möbius action over finite fields, for any known self-dual GRS codes, we give a systematic way to construct new self-dual GRS codes with flexible evaluation points.
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The authors would like to thank the Editor in Chief Prof. C. Carlet and two anonymous reviewers for their invaluable suggestions and comments which have greatly improved this article.
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This research is supported in part by National Key Research and Development Program of China under Grants 2018YFB1800204 and 2018YFA0704703, the National Natural Science Foundation of China under Grants 61771273, 61971243, 11971321, the China Postdoctoral Science Foundation under Grant 2020M670330, Guangdong Basic and Applied Basic Research Foundation under Grant 2019A1515110904, the Fundamental Research Funds for the Central Universities, Nankai University, the Natural Science Foundation of Tianjin (20JCZDJC00610).
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Fang, W., Zhang, J., Xia, ST. et al. New constructions of self-dual generalized Reed-Solomon codes. Cryptogr. Commun. 14, 677–690 (2022). https://doi.org/10.1007/s12095-021-00549-0
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DOI: https://doi.org/10.1007/s12095-021-00549-0