A study of cyclic and constacyclic codes over \(\mathbb Z_{4} + u\mathbb Z_{4} + v\mathbb Z_{4}\) (Q1993396)

Summary: In this paper, we study some properties of cyclic and constacyclic codes over the ring \(R = \mathbb Z_{4} + u\mathbb Z_{4} + v\mathbb Z_{4}\) where \(u^{2} = v^2 = uv = vu = 0\). The generator polynomials and minimal spanning set for cyclic codes over \(R\) are determined. Further, \((1 + 2u)\)-constacyclic codes are considered and find the cyclic, quasi-cyclic and permutation equivalent to a QC code over \(\mathbb Z_{4}\) as the Gray images of \((1 + 2u)\)-constacyclic codes over \(R\).