Optimal binary codes from trace codes over a non-chain ring

We construct an infinite family of two-Lee-weight codes over the ring F2+uF2+vF2+uvF2. These codes are defined as trace codes and have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Then, taking Gray mapping, we obtain an infinite family of abelian binary two-weight codes which are shown to be optimal by application of the Griesmer bound. Moreover, an application to secret sharing schemes is given.