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).