Let $p$ be a prime number and $q=p^{s}$ for a positive integer $s$. For any positive divisor $e$ of $q-1$ , we construct infinite families of codes $\mathcal {C}$ of size $q^{2m}$ with few Lee-weight. These codes are defined as trace codes over the ring $R= \mathbb {F}-{q} + u \mathbb {F}-{q}$ , $u^{2} = 0$. Using Gaussian sums, their Lee weight distributions are provided. In particular, when $\gcd (e,m)=1$ , under the Gray map, the images of all codes in $\mathcal {C}$ are of two-weight over the finite field $\mathbb {F}-{q}$ , which meet the ...
