Hulls of cyclic codes over Z4

The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of odd length n over the ring Z(4) have been focused on. Their characterization has been established in terms of the generators viewed as ideals in the quotient ring Z(4)[X] (X-n(-1)). An algorithm for computing the types of the hulls of cyclic codes of arbitrary odd length over Z(4) has been given. The 2-dimensions of the hulls of cyclic codes of length n over Z(4) and the number of cyclic codes of length n over Z(4) having hulls of a given 2-dimension are determined. The average 2-dimension E(n) of the hulls of cyclic codes of odd length n over Z(4) has been established. A general formula for E(n) has been established together with its upper and lower bounds. It turns out that E(n) grows the same rate as n. A brief discussion on hulls of cyclic codes over Z(p2), where p is an odd prime, is provided as well. (C) 2019 Elsevier B.V. All rights reserved.