LSFR BerlekampMassey和m序列一定不同吗？

lilianjie

把5个寄存器的试了两种，都不是32-1=31，都不是m序列
S:= [GF(2)| 1,1,0,0,1];
S;

BerlekampMassey(S);
ConnectionPolynomial(S);
CharacteristicPolynomial(S);

C<D>, L := BerlekampMassey(S);
C;
LFSRStep(C, S);
LFSRSequence(C, S, 100);

[ 1, 1, 0, 0, 1 ]
$.1^3 + $.1^2 + 1
3
$.1^3 + $.1^2 + 1
3
$.1^3 + $.1^2 + 1
3
D^3 + D^2 + 1
[ 1, 0, 0, 1, 0 ]
[ 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1,
0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0,
1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0,
0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1 ]








S:= [GF(2)| 1,0,0,1,1];
S;

BerlekampMassey(S);
ConnectionPolynomial(S);
CharacteristicPolynomial(S);

C<D>, L := BerlekampMassey(S);
C;
LFSRStep(C, S);
LFSRSequence(C, S, 100);

[ 1, 0, 0, 1, 1 ]
$.1^3 + $.1 + 1
3
$.1^3 + $.1 + 1
3
$.1^3 + $.1 + 1
3
D^3 + D + 1
[ 0, 0, 1, 1, 1 ]
[ 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1,
1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1,
1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0,
1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0 ]

[ 1, 0, 0, 1, 0 ]
$.1^3 + 1
3
$.1^3 + 1
3
$.1^3 + 1
3
D^3 + 1
[ 0, 0, 1, 0, 0 ]
[ 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1 ]


[ 1, 0, 1, 1, 0 ]
$.1^2 + $.1 + 1
2
$.1^2 + $.1 + 1
2
$.1^2 + $.1 + 1
2
D^2 + D + 1
[ 0, 1, 1, 0, 1 ]
[ 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,
1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,
1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,
1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1 ]


只有这个31步=2^5-1 周期最大   可分圆多项式=特征多项式D^2 + D + 1。。。 最高次不是5？？？？



[ 1, 1, 0, 1, 0 ]
$.1^3 + $.1 + 1
3
$.1^3 + $.1 + 1
3
$.1^3 + $.1 + 1
3
D^3 + D + 1
[ 1, 0, 1, 0, 0 ]
[ 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0,
0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1,
0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0,
1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1 ]


[ 1, 1, 1, 1, 0 ]
$.1^4 + $.1 + 1
4
$.1^4 + $.1 + 1
4
$.1^4 + $.1 + 1
4
D^4 + D + 1
[ 1, 1, 1, 0, 1 ]
[ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0,
1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1,
1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,
1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0 ]

还试了很多，可没一个能出5次本原多项式的。。。。LSFR BerlekampMassey和m序列一定不同吗？周期最大的 BerlekampMassey=31却不是m序列，为何？

xixiai10jk

论坛有很多新闻到这里了，也不错哦。