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

In this paper, we study Z₂Z₄-additive cyclic codes. These codes are identified as Z₄[x]-submodules of the ring R_r,s=Z₂[x]/〈x^r-1〉×Z₄[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 Z₄[x]-submodule of the ring R_r,s is determined. We show that the duals of Z₂Z₄-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 Z₂Z₄-additive cyclic codes.