Some properties of random numbers generated by Tausworthe-Lewis-Payne (TLP) method are described.
It is shown that the generated random number
wi has the same period as that of
n-th order M-sequence, unless the starting matrix
W0 which consists of
w0,
w1, …,
wn-1, is zero matrix. In order for
wi to be uniform in the sense that
W0 appears only once in a period, it is necessary that
W0 has independent columns, which is guaranteed if the delay between rows
r is such that (
r,
N)=1, where
N=2
n-1, the period of the M-sequence.
The autocorrelation function φ
ww(
k) of
wi is shown to be obtained from sampling, every
d digits, the autocorrelation function φ
xx(
k) of the binary
L-tuples from the original Msequence. Namely, φ
ww(
k)=φ
xx(
kd) where
r·d=1 (mod
N).
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