$\BBZ_{2}\BBZ_{4}$ -Additive Cyclic Codes

In this paper, we study Z
₂
Z
₄
-additive cyclic codes. These codes are identified as Z
₄
[x]-submodules of the ring R
_r,s
=Z
₂
[x]/〈x
^r
-1〉×Z
₄
[x]/〈x
^s
-1〉. The algebraic structure of this family of codes is studied and a set of generator polynomials for this family as a Z
₄
[x]-submodule of the ring R
_r,s
is determined. We show that the duals of Z
₂
Z
₄
-additive cyclic codes are also cyclic. We also present an infinite family of Maximum Distance separable with respect to the singleton bound codes. Finally, we obtain a number of binary linear codes with optimal parameters from the Z
₂
Z
₄
-additive cyclic codes.