turkmath.org

In this talk, I will mention some of the recent work I have done with different collaborators on the ring $\mathbb{Z}_{4}+u\mathbb{Z}_{4}$, a non-chain extension of the ring $\mathbb{Z}_{4}$. After mentioning some of the basic properties of the ring, defining the Lee weight and establishing the MacWilliams Identities, I will consider cyclic codes over this ring. It turns out that the Gray images of cyclic codes over $\mathbb{Z}_{4}+u\mathbb{% Z}_{4}$, which are all 2-Quasicyclic $\mathbb{Z}_{4}$-codes, are a rich source of good $\mathbb{Z}_{4}$-codes many of which are new additions to the database of known $\mathbb{Z}_{4}$-codes