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We study complementary information set codes of length \begin{document}$tn$\end{document} and dimension \begin{document}$n$\end{document} of order \begin{document}$t$\end{document} called ( \begin{document}$t-$\end{document} CIS code for short). Quasi-cyclic (QC) and quasi-twisted (QT) \begin{document}$t$\end{document} -CIS codes are enumerated by using their concatenated structure. Asymptotic existence results are derived for one-generator and fixed co-index QC and QT codes depending on Artin's primitive root conjecture. This shows that there are infinite families of rate \begin{document}$1/t$\end{document} long QC and QT \begin{document}$t$\end{document} -CIS codes with relative distance satisfying a modified Varshamov-Gilbert bound. Similar results are defined for the new and more general class of quasi-polycyclic codes introduced recently by Berger and Amrani.

advances in mathematics of communications

Long quasi-polycyclic &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$t-$\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; CIS codes