Cyclic codes over the ring GR(pe, m)[u]/ ⟨uk⟩
Cyclic codes over the ring GR(pe, m)[u]/ ⟨uk⟩
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 as an example.