On cyclic codes over $\mathbb{Z}_q+u\mathbb{Z}_q$
نویسندگان
چکیده
Let R = Zq + uZq, where q = p s and u = 0. In this paper, some structural properties of cyclic codes and quasi-cyclic (QC) codes over the ring R are considered. A QC code of length ln with index l over R is viewed both as in the conventional row circulant form and also as an R[x]/(xn − 1)-submodule of GR(R, l)[x]/(xn − 1), where GR(R, l) is the Galois extension ring of degree l over R. A necessary and sufficient condition for cyclic codes over the ring R to be free is obtained and a BCH-type bound for them is also given. A sufficient condition for 1-generator QC codes to be R-free is given. Some distance bounds for 1-generator QC codes are also discussed. The decomposition and dual of QC codes over R are also briefly discussed.
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