Open AccessGeneric constructions of MDS Euclidean self-dual codes via GRS codes
Author(s) -
Ziteng Huang,
Weijun Fang,
Fang-Wei Fu,
Fengting Li
Publication year - 2023
Publication title -
advances in mathematics of communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.601
H-Index - 26
eISSN - 1930-5346
pISSN - 1930-5338
DOI - 10.3934/amc.2021059
Subject(s) - mathematics , euclidean geometry , combinatorics , discrete mathematics , algebra over a field , pure mathematics , geometry
Recently, the construction of new MDS Euclidean self-dual codes has been widely investigated. In this paper, for square \begin{document}$ q $\end{document} , we utilize generalized Reed-Solomon (GRS) codes and their extended codes to provide four generic families of \begin{document}$ q $\end{document} -ary MDS Euclidean self-dual codes of lengths in the form \begin{document}$ s\frac{q-1}{a}+t\frac{q-1}{b} $\end{document} , where \begin{document}$ s $\end{document} and \begin{document}$ t $\end{document} range in some interval and \begin{document}$ a, b \,|\, (q -1) $\end{document} . In particular, for large square \begin{document}$ q $\end{document} , our constructions take up a proportion of generally more than 34% in all the possible lengths of \begin{document}$ q $\end{document} -ary MDS Euclidean self-dual codes, which is larger than the previous results. Moreover, two new families of MDS Euclidean self-orthogonal codes and two new families of MDS Euclidean almost self-dual codes are given similarly.