Spectral properties of (d, k) codes with multiple spacing

The multiple spaced (d, k) codes seem to have some application value for magnetic recording and magneto-optic recording systems. Recently it was shown that these codes have a performance advantage when a partial-response channel is considered. In this paper we will show that the multiple spaced (d, k) constraint has some interesting spectral properties. Certain choices of d and the spacing parameter will result in spectral nulls in the power spectrum. From these results it is shown that the previous choices of d and the spacing parameter are not optimal in terms of matching the spectral null of the sequence and that of the partial-response channel