Open AccessOptimal quinary negacyclic codes with minimum distance four
Author(s) -
Jinmei Fan,
Yanhai Zhang
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.2021043
Subject(s) - quinary , mathematics , generator (circuit theory) , polynomial , combinatorics , finite field , discrete mathematics , polynomial code , block code , linear code , mathematical analysis , algorithm , power (physics) , materials science , physics , decoding methods , alloy , quantum mechanics , composite material
Based on solutions of certain equations over finite yields, a necessary and sufficient condition for the quinary negacyclic codes with parameters \begin{document}$ [\frac{5^m-1}{2},\frac{5^m-1}{2}-2m,4] $\end{document} to have generator polynomial \begin{document}$ m_{\alpha^3}(x)m_{\alpha^e}(x) $\end{document} is provided. Several classes of new optimal quinary negacyclic codes with the same parameters are constructed by analyzing irreducible factors of certain polynomials over finite fields. Moreover, several classes of new optimal quinary negacyclic codes with these parameters and generator polynomial \begin{document}$ m_{\alpha}(x)m_{\alpha^e}(x) $\end{document} are also presented.