Properties ofPN^2sequences (Corresp.)

A method for generating sequences that approximate binary random sequences with the probability of a 1 equal to 1/4 is described. These are called
PN^2
sequences.
PN^2
sequences are generated by clocking a
PN
sequence generator at the l's of a
PN
sequence. The
PN^2
sequence is 1 when the generator output makes a transition and is 0 otherwise. It is shown that
PN^2
sequences have period
N^2
if the
PN
sequence generators have period
N
. The density of l's is shown to approach 1/4 for large
N
. It is shown that the normalized out-of-phase pulse-coincidence autocorrelation function can never exceed 1/2 or be less than 1/4 and is 1/4 most of the time for large
N
.