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A ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive code ${\calC}\subseteq{\mathbb{Z}}_2^\alpha\times{\mathbb{Z}}_4^\beta$ is called cyclic ifthe set of coordinates can be partitioned into two subsets, the set of${\mathbb{Z}}_2$ and the set of ${\mathbb{Z}}_4$ coordinates, such that anycyclic shift of the coordinates of both subsets leaves the code invariant.These codes can be identified as submodules of the $\mathbb{Z}_4[x]$-module$\mathbb{Z}_2[x]/(x^\alpha-1)\times\mathbb{Z}_4[x]/(x^\beta-1)$. The parametersof a ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive cyclic code are stated in terms ofthe degrees of the generator polynomials of the code. The generator polynomialsof the dual code of a ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive cyclic code aredetermined in terms of the generator polynomials of the code ${\cal C}$.

Z2Z4-additive cyclic codes, generator polynomials and dual codes