Two New Families of Two-Weight Codes.

We construct two new infinite families of trace codes of dimension 2m , over the ring \mathbb {F}_{p}+u\mathbb {F}_{p} , with u^{2}=u , when p is an odd prime. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. By Gray mapping, we obtain two infinite families of linear p -ary codes of respective lengths and 2(p^m-1)^2 . When m is singly even, the first family gives five-weight codes. When m is odd and p\equiv 3 \pmod {4} , the first family yields p$ -ary two-weight codes, which are shown to be optimal by application of the Griesmer bound. The second family consists of two-weight codes that are shown to be optimal, by the Griesmer bound, whenever $p=3$ and $m \ge 3$ , or $p\ge 5$ and $m\ge 4$ . Applications to secret sharing schemes are given. [ABSTRACT FROM PUBLISHER]