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BY (11) 8973
(13) C1
(46) 2007.02.28
(19)
(12)
7
(51) G 06F 7/00
(54)
(21)
(22) 2004.10.27
(43) 2005.06.30
(71)
:
: a 20040995
(73)
(BY)
(BY)
(72)
:
:
-
;
(BY)
(56) BY 3300 C1, 2000.
BY 3031 C1, 1999.
BY 5171 C1, 2003.
RU 2047892 C1, 1995.
US 4417305, 1983.
(57)
,
-
,
,
,
,
,
i,
( i = 1,15 )
(i + 1)(j = 1, 2, 3)
, j, j-
BY 8973 C1 2007.02.28
(i + 1)j-
BY 8973 C1 2007.02.28
j-
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[1].
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[2].
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,
,
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,
,
i-
(i = 1,15 )
,
.
j-
(i + 1)-
-
j-
-
(i + 1) (j = 1, 2, 3)
, j-
j-
.
,
,
,
,
2
-
BY 8973 C1 2007.02.28
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-
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1
3-17,
19, 20 21,
2,
-
18,
22, 23
25-40
24,
41.
.
: G sh = (h,h,...,h) h∈{0,1},
s,
G ≡ ∅.
h
0
F = F(X), X = (
ƒ = ƒ(X)
X
X1 = m , X 2 = n − m
(m, n-m).
. ƒ = ƒ(X) = ƒ(Xl,X2),
(ƒ),
L = (m+l)(n-m+1)
:
C( ƒ ) = (C , C ,..., C
00
01
0 ,n − m
10
1
2,..., n),
(
.),
X.
.F
1
0
πi = F(G i , G n−i ), 0 ≤ i ≤ n .
π(F)=( π0, π1, …, πn),
(
.),
X1 X2,
ƒ
,
1
2.
: 1 = (xl,x2,...,xm), 2 = ( m+1, m+2,..., n), 1≤m≤n.
,
.ƒ
n
-
(m, n-m),
11
1,n − m
, C , C ,..., C
m0
m1
,..., C , C ,..., C
Cij = ƒ (G1i , G 0m−i , G1j , G 0n −m− j ), 0 ≤ i ≤ m, 0 ≤ j ≤ n − m.
.
(m, n-m)
2L.
X1 = ( x 1 , x 2 ,..., x m ), X 2 = ( x m+1 , x m +2 ,..., x n )
.
:
i
i
E m = E m ( X1 ) i,
( 1,
j
j
E n − m = E n −m ( X 2 ) -
m ,n −m
(1)
),
2,...,
m),
0≤i≤m;
-
( x m+1 , x m+2 ,..., x n ), 0 ≤ j ≤ n − m .
j,
3
BY 8973 C1 2007.02.28
E 0n (X1 ) = E n0 − m (X 2 ) ≡ 0 .
.. ƒ= ƒ (X1, X2)
,
(m,n-m)
:
m
n−m
∑ ⊕ ∑ ⊕( E
ƒ = ƒ (X) = ƒ (X1 , X 2 ) =
i =0
i
m
j
(X1 ) ∨ E n − m (X 2 ) ∨ α ij ),
(2)
j= 0
αij∈{0, 1} ,
(ƒ).
n=6 m=3
. ƒ = ƒ (X1,X2), X1 = (x1, x2, x3), 2 = ( 4, 5, 6),
(1)
:
00
01
02
03
10
11
12
13
20
21
22
23
30
31
32
33
C( ƒ ) = C , C , C , C , C , C , C , C , C , C , C , C , C , C , C , C .
C
ij
(
= ƒ (G , G
1
i
0
3−i
1
j
,G ,G
0
3− j
) , 0 ≤ i ≤ 3, 0 ≤ j ≤ 3 .
(
-
(3, 3)
-
)
. ƒ = ƒX1,X2)
(2)
:
(3,3)
) (
) (
)
ƒ = ƒ (X1 , X 2 ) = α 00 ⊕ α 01 ∨ E1 (X 2 ) ⊕ α02 ∨ E 2 (X 2 ) ⊕ α 03 ∨ E 3 (X 2 ) ⊕
(
⊕ (α
⊕ (α
⊕ (α
) (
) (
)
∨ E (X ) ∨ E (X ) )⊕ (α ∨ E (X )) ⊕ (α ∨ E (X ) ∨ E (X )) ⊕
(3)
∨ E (X ) ∨ E (X ) )⊕ (α ∨ E (X ) ∨ E (X ) )⊕ (α ∨ E (X ) )⊕
∨ E (X ) ∨ E (X ) )⊕ (α ∨ E (X ) ∨ E (X )) ⊕ (α ∨ E (X ) ∨ E (X ) ) ,
⊕ α10 ∨ E1 (X1 ) ⊕ α11 ∨ E1 (X1 ) ∨ E1 (X 2 ) ⊕ α12 ∨ E1 (X1 ) ∨ E 2 (X 2 ) ⊕
13
22
31
1
1
3
2
1
2
3
1
1
2
20
2
2
2
23
2
32
1
1
3
2
21
3
1
2
1
2
2
1
30
33
2
3
3
1
1
3
2
E1 (X1 ) = x1 ⊕ x 2 ⊕ x 3 = x1 ⊕ x 2 ⊕ x 3 ,
E1 (X 2 ) = x 4 ⊕ x 5 ⊕ x 6 = x 4 ⊕ x 5 ⊕ x 6 ,
E 2 ( X1 ) = x 1 x 2 ⊕ x 1 x 3 ⊕ x 2 x 3 = x 1 x 2 ⊕ x 1 x 3 ⊕ x 2 x 3 ,
E 2 (X 2 ) = x 4 x 5 ⊕ x 4 x 6 ⊕ x 5 x 6 = x 4 x 5 ⊕ x 4 x 6 ⊕ x 4 x 6 ,
E 3 ( X1 ) = x 1 x 2 x 3 = x 1 ∨ x 2 ∨ x 3 ,
E3 (X 2 ) = x 4 x 5 x 6 = x 4 ∨ x 5 ∨ x 6 ;
A( ƒ ) = (α 00 , α 01 , α 02 , α 03 , α10 , α11 , α12 , α13 , α 20 , α 21 , α 22 , α 23 , α30 , α31 , α32 , α33 ,) .
(ƒ)
C(ƒ)
. ƒ
:
33
α 00 = C ; α 01 = C
32
⊕ C33 ; α 02 = C
31
⊕ C 33 ; α 03 = C 30 ⊕ C31 ⊕ α 01 ; α10 = C
21
23
-
⊕ C 33 ;
23
31
33
20
21
22
23
22
23
α11 = C ⊕ C ⊕ α 01 ; α12 = C ⊕ C ⊕ C ⊕ C ; α13 = C ⊕ C ⊕ C ⊕ C ⊕ α 03 ;
13
α 20 = C ⊕ C33 ; α 21 = C12 ⊕ C13 ⊕ α 01 ; α 22 = C11 ⊕ C31 ⊕ α 20 ;
α 23 = C ⊕ C ⊕ C ⊕ C ⊕ α 03 ; α30 = C ⊕ C ⊕ α 20 ;
10
11
12
13
03
23
α31 = C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ α 01;
02
03
12
13
22
23
α32 = C 01 ⊕ C 03 ⊕ C11 ⊕ C 21 ⊕ C 23 ⊕ C 31 ⊕ α 20 ;
α33 = C 00 ⊕ C 01 ⊕ C 02 ⊕ C 03 ⊕ C10 ⊕ C11 ⊕ C12 ⊕ C13 ⊕ α13 .
4
BY 8973 C1 2007.02.28
,
E 3 (X1 ) = E1 (X1 ) ∨ E 2 (X1 )
E 3 (X 2 ) = E1 (X 2 ) ∨ E 2 (X 2 ) .
: s1 = E 1 (X1 ), s 2 = E1 (X 2 ), p1 = E 2 (X1 ), p 2 = E 2 (X 2 ) .
E 3 ( X 1 ) = s 1 ∨ p1
,
E 3 (X 2 ) = s 2 ∨ p 2 .
(3)
:
ƒ = ƒ (X1 , X 2 ) = α 00 ⊕ (α 01 ∨ s 2 ) ⊕ (α 02 ∨ p 2 ) ⊕ (α 03 ∨ s 2 ∨ p 2 ) ⊕ (α10 ∨ a1 ) ⊕
⊕ (α11 ∨ s1 ∨ s 2 ) ⊕ (α12 ∨ s1 ∨ p 2 ) ⊕ (α13 ∨ s1 ∨ s 2 ∨ p 2 ) ⊕ ( α 20 ∨ p1 ) ⊕
(4)
⊕ (α 21 ∨ p1 ∨ s 2 ) ⊕ ⊕(u 22 ∨ p1 ∨ p 2 ) ⊕ (α 23 ∨ p1 ∨ s 2 ∨ p 2 ) ⊕ (α30 ∨ s1 ∨ p1 ) ⊕
⊕ (α 31 ∨ s1 ∨ p1 ∨ s 2 ) ⊕ (α 32 ∨ s1 ∨ p1 ∨ p 2 ) ⊕ (α33 ∨ s1 ∨ p1 ∨ s 2 ∨ p 2 )
,
s1(s2)
p1(p2)
,
2).
1
.
(3,3)
U = (u0, u1,..., u15)
(4).
.
. U = (ƒ).
,
-
(ƒ)
-
.
19, 20
1,
2
3 (
25-40
. ƒ = ƒ (X1,X2),
4,
5
21
),
6 (
u0-u15
22, 23
24
).
-
.
41
U = (u0, u1,..., u15).
U
-
ƒ = ƒ ( X ) = x 1x 2 x 3 ∨ x 1 x 2 x 3 ∨ x 1 x 2 x 3 ∨ x 1 x 2 x 3 x 4 x 5 x 6 ∨ x 1x 2 x 3 x 4 x 5 x 6 .
,
.
:
00
01
02
03 10
11 12
13
20
21
C( ƒ ) = C , C , C , C , C , C , C , C , C , C , C 22 , C 23 , C 30 , C 31 , C 32 , C 33 . =
= (0, 0, 0,1, 0, 0, 0, 0,1,1, 1,1, 1, 0, 0, 0 ).
(ƒ) (
. ƒ):
α00 = 1, α01 = 1, α 02 = 1, α 03 = 0, α10 = 0, α11 = 1, α12 = 1, α13 = 0, α 20 = 1, α 21 = 1, α 22 = 1,
(
)
α 23 = 0, α30 = 1, α 31 = 0, α32 = 0, α33 = 1.
U = (ƒ),
1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1).
,
-
-
: U = (u0, u1,..., u15) = (1,
.
25, 26, 27, 30, 31, 33, 34, 35, 37
28, 29, 32, 36, 38 39.
40;
-
.
:
1.
2.
3031,
3300,
G 06 F 7/00, 1999.
G 06 F 7/00, 2000 (
).
. 220034, .
5
,
.
, 20.
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