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Title: On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉
Authors: Hai Q. Dinh
Abhay Kumar Singh
Pratyush Kumar
Songsak Sriboonchitta
Keywords: Mathematics
Issue Date: 1-Aug-2018
Abstract: © 2018 Elsevier B.V. In this paper, we consider cyclic codes of odd length n over the local, non-chain ring R=Z2s[u]∕〈uk〉 = Z2s+uZ2s+…+uk−1Z2s(uk=0), for any integers s≥1 and k≥2. An explicit algebraic representation of such codes is obtained. This algebraic structure is then used to establish the duals of all cyclic codes. Among others, all self-dual cyclic codes of odd length n over the ring R are determined. Moreover, some examples are provided which produce several optimal codes.
ISSN: 0012365X
Appears in Collections:CMUL: Journal Articles

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