Nonlinear Feedforward Sequences of m-Sequences II

• Zongduo Dai
• Xuning Feng
• Mulan Liu
• Zhe-Xian Wan
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)

Abstract

Let
$$\alpha \; = \;\left( {a_0 ,a_1 ,a_2 , \ldots } \right)$$
be a given n-stage m-sequence over the binary field F2, whose minimal polynomial will be denoted by f(x). We know that f(x) is primitive and of degree n. Denote $${{{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{s}}}_{i}} = ({{a}_{i}},{{a}_{{i + 1}}}, \ldots ,{{a}_{{i + n - 1}}})$$, i ≥ 0 and call $${{{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{s}}}_{i}}$$ the i-th state of the n-stage m-sequence α. Let
$$\phi \; = \;\sum\limits_{i_1 ,i_2 , \ldots ,i_n = 0}^1 {a_{i_1 \;i_2 \ldots i_n } } \;x_1^{i_1 } x_2^{i_2 } \ldots x_n^{i_n } ,\;a_{i_1 \;i_2 \ldots i_n } \; \in \;{\text{F}}_{\text{2}},$$
be a Boolean polynomial in n variables x 1,..., x n and of degree r. Obviously r ≤ n.

References

1. [1]
Dai, Z., Feng, X., Liu, M. and Wan, Z., Nonlinear feedforward sequences of m-sequences, Proc. of 1988 Beijing International Workshop on Information Theory, July 4–7 (1988), A-2.1-A-2.8.Google Scholar
2. [2]
Zierler, N., Linear recurring sequences, J. Soc. Indust. Appl. Math., 7 (1959) 31–48.

© Springer-Verlag New York, Inc. 1990

• Zongduo Dai
• 1
• Xuning Feng
• 2
• Mulan Liu
• 3
• Zhe-Xian Wan
• 3