Long quasi-polycyclic $t-$CIS codes

Abstract

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