Decimations of the Frank-Heimiller Sequences

The Frank-Heimiller sequence of period N
²
with
N
phases is constructed by writing the
N
by
N
discrete Fourier transform matrix by rows. The periodic autocorrelation sidelobes for such a sequence are all zero. Small families of
N
-phase sequences, with optimal periodic cross correlations, can be formed by judicious selection of decimations of the Frank-Heimiller sequence.