The Permutation Groups and the Equivalence of Cyclic and Quasi-Cyclic Codes

Abstract: We give the class of finite groups which arise as the permutation groups of cyclic codes over finite fields. Furthermore, we extend the results of Brand and Huffman et al. and we find the properties of the set of permutations by which two cyclic codes of length p^r can be equivalent. We also find the set of permutations by which two quasi-cyclic codes can be equivalent.