Phase normalised m-sequences with the inphase decimation property {m(k)}={m(2k)}

The inphase decimation property of a binary sequence {f(k)} is defined such that f(k)=f(2k) for all k=0, 1, 2,¿ Given a primitive generator polynomial G(D) of degree r with its even and odd parts Ge(D) and Go(D), it is shown that there is a unique version of the corresponding m-sequence with this inphase decimation property, resulting as Ge(D)/G(D) if r is odd and Go(D)/G(D) if r is even. An m-sequence in such a phase position is termed the phase normalised version.