Weight distribution of some reducible cyclic codes

Let q=pm where p is an odd prime, m 3, k 1 and gcd(k,m)=1. Let Tr be the trace mapping from to and . In this paper we determine the value distribution of following two kinds of exponential sums and where is the canonical additive character of . As an application, we determine the weight distribution of the cyclic codes and over with parity-check polynomial h2(x)h3(x) and h1(x)h2(x)h3(x), respectively, where h1(x), h2(x) and h3(x) are the minimal polynomials of π−1, π−2 and π−(pk+1) over , respectively, for a primitive element π of .