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In this paper, we study cyclic codes over the ring R = Z4 + uZ4 + u 2 Z4 , where u 3 = 0 . We investigate Galois extensions of this ring and the ideal structure of these extensions. The results are then used to obtain facts about cyclic codes over R . We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over Z4 by considering Gray images of cyclic codes over R .

In this work, skew quasi cyclic codes over [Formula: see text], where [Formula: see text] are considered. The generating set for one generator skew quasi cyclic codes over [Formula: see text] is also determined. We discuss a sufficient condition for one generator skew quasi cyclic codes to be free. Furthermore, a BCH type bound is given for free one generator skew quasi cyclic codes. We investigate the dual of skew quasi cyclic codes over [Formula: see text]. We give a necessary and sufficient condition for skew cyclic codes over [Formula: see text] to contain its dual. Moreover, we construct quantum codes from skew cyclic codes over [Formula: see text]. By using computer search we give some examples about skew quasi cyclic codes and list some quantum parameters in the table.

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