Double cyclic codes over 𝔽q + u𝔽q + u2𝔽q. (2015) - Yao, Ting; Shi, Minjia; Solé, Patrick
A double cyclic code of length (r, s) over a chain ring R is a set that can be partitioned into two parts that any cyclic shift of the coordinates of both parts leaves invariant the code. These codes can be viewed as R[x]-submodules of R r × R s . In this paper, the generator polynomials of this family of codes as R[x]-submodules of R r × R s are determined. Further, the minimal generating sets of this family of codes as R-submodules of R r × R s are obtained. Finally, we show the relationship of generators between the double cyclic code and its dual.