… 4, we determine the dual code of each cyclic code of length n over R and investigate self-duality
for such codes… cyclic codes of length kn and index k over \(\mathbb {Z}_{4}\) derived from …

… introduce a family of binary linear cyclic codes which are Gray images of 4-linear negacyclic
codes. … We also prove that, if n is odd, then the Gray image of a linear cyclic code over 4 of …

… cyclic codes of length n=2 e , for any positive integer e is considered. We show that any cyclic
code is an ideal in the ring R n =Z 4 … as we will show is not as easy as in the case for odd n. …

… for cyclic codes over Z4 for lengths of the form 2n where n is odd. The case for odd n follows
… the classification by examining cyclic codes over Z4 of length N =2kn, where n is odd. Our …

… mainly focused on cyclic codes of odd length over R which are … for principally generated
cyclic codes of odd lengths over R to … IV, we have studied cyclic codes of odd length over R. The …

… of cyclic codes of length 2n (ie, oddly even length) over the ring Z 4 of integers modulo 4 by
viewing these codes as … on cyclic codes of length N = 2 n over Z 4 , where n is an odd positive …

… Theorem 2: Suppose C is a Z4-cycIic code of odd length n. Then there are unique, monic
polynomials f, g, and h such that C = (fh.2fg). where fgh = 2' - 1, and IC1 = 4deRg2degh. …

… A complete structure of cyclic codes over Z4 of odd length has … to cyclic codes of arbitrary
even length over Z4. Recently, Yildiz and Karadeniz [19] have studied linear codes over R = Z4 …

… of cyclic codes and cyclic self-dual codes over R. Since FF2 is a subring of R, the minimum
distance of a lifted cyclic code over … We assume that n is odd and we represent codewords by …

… 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 …