Some results on cyclic codes over \(\mathbb{Z}_q + u\mathbb{Z}_q\) (Q2788736)

Let \(R=\mathbb Z_q+u\mathbb Z_q\), where \(q=p^s\) for some prime \(p\) and \(u^2=0\). Authors have obtained the minimum generating sets of cyclic codes over \(R\). A necessary and sufficient condition for cyclic codes over \(R\) to be \(R\)-free is obtained. Further it is shown that the minimum Hamming distance of a cyclic code over \(R\) satisfies a BCH-type bound like a cyclic code over a finite field.