Abstract
<p style='text-indent:20px;'>Based on solutions of certain equations over finite yields, a necessary and sufficient condition for the quinary negacyclic codes with parameters <inline-formula><tex-math id="M1">\begin{document}$ [\frac{5^m-1}{2},\frac{5^m-1}{2}-2m,4] $\end{document}</tex-math></inline-formula> to have generator polynomial <inline-formula><tex-math id="M2">\begin{document}$ m_{\alpha^3}(x)m_{\alpha^e}(x) $\end{document}</tex-math></inline-formula> is provided. Several classes of new optimal quinary negacyclic codes with the same parameters are constructed by analyzing irreducible factors of certain polynomials over finite fields. Moreover, several classes of new optimal quinary negacyclic codes with these parameters and generator polynomial <inline-formula><tex-math id="M3">\begin{document}$ m_{\alpha}(x)m_{\alpha^e}(x) $\end{document}</tex-math></inline-formula> are also presented.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory,Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory
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