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Cyclic codes over the ring GR(pe, m)[u]/ ⟨uk

Authors: 

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

Source title: 
Discrete Mathematics, 343(1): 111543, 2020 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

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 s as an example.