Some constructions of (almost) optimally extendable linear codes

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula> be a generator matrix of linear code id="M2">\begin{document}$ \mathcal C and id="M3">\begin{document}$ [G: I_k] its extendable id="M4">\begin{document}$ {C}' $\end{document}</tex-math></inline-formula>, we call id="M5">\begin{document}$ is optimally (almost optimally) if id="M6">\begin{document}$ d(\mathcal C^\perp) = d({\mathcal C'}^\perp) $\end{document}</tex-math></inline-formula>(<inline-formula><tex-math id="M7">\begin{document}$ very close to id="M8">\begin{document}$ respectively), where id="M9">\begin{document}$ the minimal distance dual id="M10">\begin{document}$ $\end{document}</tex-math></inline-formula>. In order safeguard susceptible information lay in registers oppose SCA FIA, it useful construct an id="M11">\begin{document}$ this paper, three classes (almost) codes: (1) irreducible cyclic codes; (2) maximum-distance-separable (MDS) codes near (NMDS) codes.</p>