Weight distributions of some binary primitive cyclic codes

Let s and k be integers such that s is a divisor of 2^k-1. Let g(x) be a divisor of x^s-1 over F₂ , and let π(x) be a primitive polynomial of degree k over F₂. We consider the binary cyclic code C of length N=2^k -1 generated by (X^N-1)/g(x)π(x). For special cases, we determine the weight distribution of C by using the weights of the cyclic code of length s generated by (x^s-1)/g(x)