Abstract
We study complementary information set codes of length tn and dimension n of order t called (t-CIS code for short). Quasi-cyclic (QC) and quasi-twisted (QT) t-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 1/t long QC and QT t-CIS codes with relative distance satisfying a modified Varshamov-Gilbert bound. Similar results are de fined for the new and more general class of quasi-polycyclic codes introduced recently by Berger and Amrani.