WEIGHT DISTRIBUTIONS OF SOME BINARY PRIMITIVE CYCLIC CODES

Let s and k be integers such that s is a divisor of 2k - 1. Let g(x) be a divisor of x(s) - 1 over F2, and let pi(x) be a primitive polynomial of degree k over F2. We consider the binary cyclic code C of length N = 2k - 1 generated by (x(N) - 1)/g(x)pi(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).