Z2Z4-Additive Cyclic Codes, Generator Polynomials, and Dual Codes

A Z(2)Z(4)-additive code C subset of Z(2)(alpha) x Z(4)(beta) is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z(2) and the set of Z(4) coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the Z(4)[x]-module Z(2)[x]/(x(alpha) - 1) x Z(4)[x]/(x(beta) - 1). The parameters of a Z(2)Z(4)-additive cyclic code are stated in terms of the degrees of the generator polynomials of the code. The generator polynomials of the dual code of a Z(2)Z(4)-additive cyclic code are determined in terms of the generator polynomials of the code C.