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Title: Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉
Authors: Hai Q. Dinh
Abhay Kumar Singh
Pratyush Kumar
Songsak Sriboonchitta
Keywords: Mathematics
Issue Date: 1-Jan-2019
Abstract: © 2019 Elsevier B.V. Let R=GR(pe,m)[u]∕〈uk〉 be a finite commutative ring for a prime p and any positive integers e,m and k. In this paper, we derive the explicit representation of cyclic codes over the ring R of length n, where n and p are coprime. We also discuss the dual of such cyclic codes over the ring R and give a sufficient condition for the codes to be self-dual. Moreover, we study quasi-cyclic codes of length kn and index k over the ring R, and obtain some good codes satisfying the bound given in Dougherty and Shiromoto (2000) over the ring Z9 as an example.
ISSN: 0012365X
Appears in Collections:CMUL: Journal Articles

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