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On the structure of cyclic codes over the ring Z2s [u]/⟨u k ⟩


Hai Q. Dinh, Abhay Kumar Singh, Pratyush Kumar, Songsak Sriboonchitta

Source title: 
Discrete Mathematics, 341: 2243-2275, 2018 (ISI)
Academic year of acceptance: 

In this paper, we consider cyclic codes of odd length n over the local, non-chain ring = Z2s [u] ∕〈uk〉 = Z2+ uZ2+…+ uk−1Z2s (uk=0), for any integers ≥ 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.