In this paper, new binary cyclic codes (hereafter, refered to as GMW code) which are generated by using GMW sequence, g(t) = tr((trk(a))r), and its cyclic shifts are introduced. Code length of GMW codes is 2a-1, where k is composite integer, e·J. Dimension of the GMW codes is k(k/j)w-1, where w is a Hamming weight of r. Several properties of GMW codes such as designed distance, minimum distance, and weights of code words are obtained in terms of parameters of GMW sequences. And expansion of GMW sequences in terms of m-sequence and its decimation sequences are introduced and characteristic polynomials of GMW sequences are also derived.