TY - JOUR
T1 - The Expansion Complexity of Ultimately Periodic Sequences over Finite Fields
AU - Sun, Zhimin
AU - Zeng, Xiangyong
AU - Li, Chunlei
AU - Zhang, Yi
AU - Yi, Lin
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - The expansion complexity is a new figure of merit for cryptographic sequences. In this paper, we present an explicit formula of the (irreducible) expansion complexity of ultimately periodic sequences over finite fields. We also provide improved upper and lower bounds on the $N$ th irreducible expansion complexity when they are not explicitly determined. In addition, for some infinite sequences with given nonlinear complexity, a tighter upper bound of their $N$ th expansion complexity is given.
AB - The expansion complexity is a new figure of merit for cryptographic sequences. In this paper, we present an explicit formula of the (irreducible) expansion complexity of ultimately periodic sequences over finite fields. We also provide improved upper and lower bounds on the $N$ th irreducible expansion complexity when they are not explicitly determined. In addition, for some infinite sequences with given nonlinear complexity, a tighter upper bound of their $N$ th expansion complexity is given.
KW - Expansion complexity
KW - nonlinear complexity
KW - ultimately periodic sequence
UR - http://www.scopus.com/inward/record.url?scp=85115143575&partnerID=8YFLogxK
U2 - 10.1109/TIT.2021.3112824
DO - 10.1109/TIT.2021.3112824
M3 - Article
AN - SCOPUS:85115143575
SN - 0018-9448
VL - 67
SP - 7550
EP - 7560
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 11
ER -