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- W3111636215 abstract "Self-dual MDS codes over finite fields are linear codes with important cryptographic and combinatorial applications. In this correspondence, a different approach is proposed to obtain Hermitian self-dual MDS codes from (extended) generalized Reed-Solomon (abbreviation to GRS and EGRS) codes. The necessary and sufficient conditions of a Hermitian self-dual (extended) GRS code are presented. With the help of this new method, we revise and improve the results in Niu and Yue <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>et al.</i> (IEEE Communications Letters, 23(5): 781-784, 2019). Furthermore, we suppose that there exist Hermitian self-dual (extend) GRS codes over <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathbb {F}_{q^{2}}$ </tex-math></inline-formula> if and only if their code length <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$nleq q+1$ </tex-math></inline-formula> ." @default.
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- W3111636215 date "2021-04-01" @default.
- W3111636215 modified "2023-10-17" @default.
- W3111636215 title "Hermitian Self-Dual GRS and Extended GRS Codes" @default.
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- W3111636215 doi "https://doi.org/10.1109/lcomm.2020.3044893" @default.
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