Cyclic codes of arbitrary length over Fq + uFq + u 2 Fq + ::: + u k 1 Fq

In this paper, we study the structure of cyclic codes of an arbitrary length n over the ring Fq + uFq + u 2 Fq + ::: + u k 1 Fq, where u k = 0 and q is a power of prime. Also we study the rank for these codes, and we find their minimal spanning sets. This study is a generalization and extension of the works in references (9) and (12), the dual codes over the ring Fq +uFq +u 2 Fq, where u 3 = 0 are studied as well

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