On equivalence of cyclic codes, generalization of a quasi-twisted search algorithm, and new linear codes

Abstract

A fundamental problem in coding theory is the explicit construction of linear codes with best possible parameters. A search algorithm (ASR) on certain types of quasi-twisted (QT) codes has been very fruitful to address this challenging problem. In this work, we generalize the ASR algorithm to make it more comprehensive. The generalization is based on code equivalence. As a result of implementing the more general algorithm, we discovered 27 new linear codes over the fields $$\mathbb {F}_q$$ for $$q=3,4,5,$$ and 7. Further, we prove several useful theoretical results about the equivalence of cyclic codes, constacyclic codes, and QT codes.