Cyclic Codes and Sequences From Generalized Coulter–Matthews Function

In this paper, we will study the exponential sum SigmaxisinF_q x(alphax(p^k+1)/2+betax) that is related to the generalized Coulter-Matthews function x(pk+1)/2 with k/gcd. As applications, we obtain the following: the correlation distribution of a p-ary m-sequence and a decimated m-sequence of degree p^k+1/2; the weight distribution of the cyclic code whose dual has two zeros pi^-1 and pi^-((p^k+1)/2).