Long quasi-polycyclic t-CIS codes

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 tCIS 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.