Binary Images of Z2Z4-Additive Cyclic 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. We study the binary images of Z(2)Z(4)-additive cyclic codes. We determine all Z(2)Z(4)-additive cyclic codes with odd beta whose Gray images are linear binary codes. In this case, it is shown that such binary codes are permutation equivalent (by the Nechaev permutation) to Z(2)-double cyclic codes. Finally, the generator polynomials of these binary codes are given.