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Double cyclic codes over 𝔽q + u𝔽q + u2𝔽q
by Ting Yao; Minjia Shi; Patrick Solé
International Journal of Information and Coding Theory (IJICOT), Vol. 3, No. 2, 2015


Abstract: 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 Rr × Rs. In this paper, the generator polynomials of this family of codes as R[x]-submodules of Rr × Rs are determined. Further, the minimal generating sets of this family of codes as R-submodules of Rr × Rs are obtained. Finally, we show the relationship of generators between the double cyclic code and its dual.


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