Three weight ternary linear codes from non-weakly regular bent functions

Abstract

<p style='text-indent:20px;'>This paper constructs several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions based on a generic construction method. Instead of the whole space, we use the subspaces <inline-formula><tex-math id="M1">\begin{document}$ B_{\pm}(f) $\end{document}</tex-math></inline-formula> associated with a ternary non-weakly regular dual-bent function <inline-formula><tex-math id="M2">\begin{document}$ f $\end{document}</tex-math></inline-formula>. Unusually, we use the pre-image sets of the dual function <inline-formula><tex-math id="M3">\begin{document}$ f^* $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M4">\begin{document}$ B_{\pm}(f) $\end{document}</tex-math></inline-formula> as the defining sets of the corresponding codes. Since the size of the defining sets of the constructed codes is flexible, it enables us to construct several codes with different parameters for a fixed dimension. We represent the weight distribution of the constructed codes, and we also give several examples.</p>