Three weight ternary linear codes from non-weakly regular bent functions
Rumi Melih Pelen · Advances in Mathematics of Communications · 2022
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 \begin{document}$ B_{\pm}(f) $\end{document} associated with a ternary non-weakly regular dual-bent function \begin{document}$ f $\end{document} . Unusually, we use the pre-image sets of the dual function \begin{document}$ f^* $\end{document} in \begin{document}$ B_{\pm}(f) $\end{document} 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.