Quaternary 1-generator quasi-cyclic codes

Quaternary 1-generator quasi-cyclic codes are considered in the paper. Under the conditions that n is odd and gcd(|2|n, m) = 1, where |2|n denotes the order of 2 modulo n, we give the enumeration of quaternary 1-generator quasi-cyclic codes of length mn, and describe an algorithm which will obtain one, and only one, generator for each quaternary 1-generator quasi-cyclic code.