$\BBZ_{2}\BBZ_{4}$ -Additive Cyclic Codes
Taher Abualrub, İrfan Şiap, Nuh Aydın · IEEE Transactions on Information Theory · 2014
In this paper, we study Z2Z4-additive cyclic codes. These codes are identified as Z4[x]-submodules of the ring Rr,s=Z2[x]/〈xr-1〉×Z4[x]/〈xs-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 Rr,sis 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.