TY - JOUR
T1 - Lower and Upper Bounds on the Density of Irreducible NFSRs
AU - Jiang, Yupeng
AU - Lin, Dongdai
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2018/5
Y1 - 2018/5
N2 - A nonlinear feedback shift register (NFSR) of n -stage is called irreducible if, the family of output sequences of any NFSR of stage less than n is not included in that of the NFSR. Tian and Qi in this paper [IEEE-IT, 2013(6),4006-4012] gave a lower bound on the density of irreducible NFSRs. In this paper, we improve their lower bound and also give an upper bound on the density of irreducible NFSRs. Moreover, the gap between our upper and lower bounds is less than 0.04.
AB - A nonlinear feedback shift register (NFSR) of n -stage is called irreducible if, the family of output sequences of any NFSR of stage less than n is not included in that of the NFSR. Tian and Qi in this paper [IEEE-IT, 2013(6),4006-4012] gave a lower bound on the density of irreducible NFSRs. In this paper, we improve their lower bound and also give an upper bound on the density of irreducible NFSRs. Moreover, the gap between our upper and lower bounds is less than 0.04.
KW - algebraic normal form
KW - generalized division algorithm
KW - irreducible NFSR
KW - Nonlinear feedback shift register
KW - unique expression
UR - https://www.scopus.com/pages/publications/85040947815
U2 - 10.1109/TIT.2018.2796127
DO - 10.1109/TIT.2018.2796127
M3 - 文章
AN - SCOPUS:85040947815
SN - 0018-9448
VL - 64
SP - 3944
EP - 3952
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 5
ER -