A large class of nonlinear shift register sequences (Corresp.)

The cycle structure of a binary linear shift register with connection polynomial
G(x)=(1+x)^{2}g(x)
, where
g(x)
is a primitive polynomial of degree
m-2
over GF
(2)
, is used to give several construction techniques for generation of shift-register sequences of length
l=2^{m}-4
. It is shown that a class of nonlinear deBruijn cycles, where the number of elements is proportional to
2^{5m}
, can be constructed. The obtained cycles can be generated by simple
m
-stage nonlinear feedback shift registers.