Investigation of a family of M-sequences

A family of binary M-sequences, called primitive M-sequences, is investigated in two categories. One of the categories, autocorrelation function C(τ) of primitive M-sequences of order n is discussed, we present that C(n+1)=-4 or 0 or 4, and some other autocorrelation values for that n+1<τ<2n. Another, properties of primitive M-sequences are studied, we present the reciprocal equivalent property of primitive M-sequences, that is, the reciprocal primitive M-sequence pair has the same autocorrelation values, linear span and that components of one of the two sequences are exactly inversion of ones of another.