In this paper, we study cyclic codes over the rings Z 2 + uZ 2 and Z 2 + uZ 2 + u 2 Z 2 . We find a set of generators for these codes. The rank, the dual, and the Hamming distance of these codes are studied as well. Examples of cyclic codes of various lengths are also studied.

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In this paper we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalization of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without any restriction. Our results show that these codes are equivalent to either cyclic 1 codes or quasi-cyclic codes, hence establish strong connections with well-known classes of codes.

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