On cyclic codes over \(\mathbb{Z}_4\) + \(u\mathbb{Z}_4\) and their \(\mathbb{Z}_4\)-images (Q887829)

Summary: Linear codes over the ring \(\mathbb{Z}_4 + u\mathbb{Z}_4\) have been introduced recently. In this paper, we study cyclic codes over this ring. We determine algebraic structures of cyclic codes over \(\mathbb{Z}_4 + u\mathbb{Z}_4\) and obtain basic facts about their generators. Making use of their algebraic structure, we conducted a computer search for cyclic codes over \(\mathbb{Z}_4 + u\mathbb{Z}_4\) and obtained many new linear codes over \(\mathbb{Z}_4\). These codes have been added to the database of \(\mathbb{Z}_4\) codes.