Optimal Two-Weight Codes From Trace Codes Over $\mathbb {F}_2+u\mathbb {F}_2$

Abstract

We construct an infinite family of two-Lee-weight codes over the ring $\mathbb {F}_{2}+u\mathbb {F}_{2}$ . These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. By Gray mapping, we obtain an infinite family of abelian binary two-weight codes. They are shown to be optimal by application of the Griesmer bound. An application to secret sharing schemes is given.