A ℤ2ℤ4-additive code C ⊆ ℤ2α× ℤ4βis called cyclic if the set of coordinates can be partitioned into two subsets, the set of ℤ2coordinates and the set of ℤ4coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. Let Φ(C) be the binary Gray map image of C. We study the rank and the dimension of the kernel of a ℤ2ℤ4-additive cyclic code C, that is, the dimensions of the binary linear codes (Φ(C)) and ker (Φ(C)). We give upper and lower bounds for these parameters. It is known that the codes (Φ(C)) and ker (Φ(C)) are binary images of ℤ2ℤ4-additive codes that we denote by R(C) and K(C), respectively. Moreover, we show that R(C) and K(C) are also cyclic and determine the generator polynomials of these codes in terms of the generator polynomials of the code C.

A 762764-additive code C ⊆ ℤ2α× ℤ4βis called cyclic if the set of coordinates can be partitioned into two subsets, the set of ℤ2and the set of ℤ4coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. We study the binary images of ℤ2ℤ4-additive cyclic codes. We determine all ℤ2ℤ4-additive cyclic codes with odd β 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 ℤ2-double cyclic codes. Finally, the generator polynomials of these binary codes are given.

A ℤ2ℤ4-additive code C ⊆ ℤ2αx ℤ4βis called cyclic if the set of coordinates can be partitioned into two subsets, the set of ℤ2and the set of ℤ4coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the ℤ4[x]-module ℤ2[x]/(xα- 1) x ℤ4[x]/(xβ- 1). The parameters of a ℤ2ℤ4-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 ℤ2ℤ4-additive cyclic code are determined in terms of the generator polynomials of the code C.