Linear codes with eight weights over Fp + uFp

In this article, based on the defining set D = {x is an element of F-p*m: Tr(x) = 0}, we explore the Lee-weight distribution of linear codes C-D = {(tr(ax(2)))(x is an element of D): a is an element of F(p)m + uF(p)m} over the finite ring F-p + uF(p) with p being an odd prime and u(2) = 0. By employing the exponential and Gauss sums, we calculate the Lee weight of all possible codewords as well as their frequencies. Two classes of eight-weight linear codes are obtained, where one of them is new. We also show that for some small values m, the code C-D has two weights (m = 2) and seven weights (m = 3, 4 and p = 3).