Weight distribution of some reducible cyclic codes

Abstract: Let where p is an odd prime, , and . 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 and , respectively, where , and are the minimal polynomials of , and over , respectively, for a primitive element π of . [Copyright &y& Elsevier]