Cyclic Codes and Sequences From Generalized Coulter–Matthews Function
Jinquan Luo, Keqin Feng · IEEE Transactions on Information Theory · 2008
In this paper, we will study the exponential sum SigmaxisinFqx(alphax(pk+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 pk+1/2; the weight distribution of the cyclic code whose dual has two zeros pi-1and pi-((pk+1)/2).