On the structure of cyclic codes over the ring Z2s [u]/⟨u k ⟩
On the structure of cyclic codes over the ring Z2s [u]/⟨u k ⟩
Source title:
Discrete Mathematics, 341: 2243-2275,
2018
(ISI)
Academic year of acceptance:
2018-2019
Abstract:
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.