( ). S ( ), , :
S = Sk S2 S1 ,
Si (4) , . , Si = 0 S = 0.
1: 0110011 (. **1*011 (. 3,5,6,7 , *)). 0110001 ( 6 ). S.
S1 = b1 + b3+ b5 + b7 = 0 + 1 + 0 + 1 = 0 (mod 2),
S2 = b2 + b3+ b6 + b7 = 1 + 1 + 0 + 1 = 1 (mod 2),
S3 = b4 + b5 + b6 + b7 = 0 + 0 + 0 + 1 = 1 (mod 2).
S = 1 1 0 = 6 ( ).
2: 0111011 ( 4 () ).
S1 = b1 + b3+ b5 + b7 = 0 + 1 + 0 + 1 = 0 (mod 2),
S2 = b2 + b3+ b6 + b7 = 1 + 1 + 1 + 1 = 0 (mod 2),
S3 = b4+ b5 + b6 + b7 = 1 + 0 + 1 + 1 = 1 (mod 2).
S = S3 S2 S1= 1 0 0 = 4 ( ).
: 0110011, 1011 ( , )
, S 0 ( S , ). .
: . 2, 3, . .
å
a1 B1
a2 B2
a3 B3
.
ar Br
Bi O ={ b1,b2,b3.bq }, q O li = l (Bi) (i= 1,,r) ( ).
1 å , ( ):
(5)
2 li , (5), å¢, l (B1) = l1, , l (Br) = lr.
.
1. , l1, l2,, lr.
2. , , (3.5) .
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3 1 3 , ( 5 , ).
. , O ={ b1,b2 } {0, 1} .. q = 2. ( ) 8. ( 8 , ). r, (5) r = q 8; 28=256. , I 256 . 8 . ( ):
l = ]logq r [ ( r q). , , :
l i = l (Bi) (6)
I={ a1,a2 ,, ar } , p1, p2, pr , (6) :
(7)
, . l*.
l* = (8)
(8) å, .
l å, .
1 ≤ l ≤ ]logq r[ (9)
, ( Web ). ( l) , , l > ]log q r [ . (7) pi li ≤ ]logq r[. pi = 0 , , p* = min (pi), :
(10)
. , å l = l*, , .
. ( ) ( , ).
. å ( ), . :
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Ø ( m = 0);
Ø , q ( O), O ={ b1,b2} ( m = 1);
Ø , q, O ( m = 2);
Ø , .. ;
, , .
1 q = 3. q m ( 3, 9, 27 ..). .
, 3 , 9 .. r q m, m m . Bi , m .
,
q m < r < q m+1, (11)
( r m, ).
( ) :
m m+1 ;
m+1 m .
r :
r = ( q m n )+ q ×n t, (12)
n - m, m+1 ;
t m+1 , (t < q).
l* :
l* = [(q m n) × m + (q ×n t)(m+1)] / r (13)
I={ a1,a2 ,, ar } , p1, p2, pr , . , , , p1, p2, pr, i i+1 , . .
1 pj < pi ,
l j ³ lj.
. , m , , m +1 .
. , q. , , , , , , q, 2 ≤ q < q ( , , q = q ). r / (q 1) q (14):
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(14)
2 , .
3 ( ), q (14).
, , q .
( ) , .
1 q (14).
2 p1, p2, pr : p1, p2,.. pj, p,prqo, p = prqo+1+ + pr (.. q , ); ( q ) , q .
3 .2 ( q , O, 1 ).
4 2, 3 , , .. (, , ); , r pj. ( ), .
1: ( ) :
r | q | p1, p2, p12 |
0,26; 0,22; 0,14 |
1 q (14).
k = ]r / (q 1)[ ( )
k =] 7/2[ = 1; q0 = 3.
2 1 (7 ):
0,26; 0,22; 0,14; 0,10; 0,10; 0,09; 0,09 ( , 2).
2 (5 ) 0,28; 0,26; 0,22; 0,14; 0,10
3 (3 ) 0,46; 0,28; 0,26;
3 .2 ( 3 , O, 1 ).
4 2, 3 , , .. (, , ); , r pj. ( ), .
:
l* = = 0,26 + (0,28+0,46)2 = 1,74.
2: ( ) :
r | q |
q =3; r = 7 (12) m = 1. 1 2 (. . 3).
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r = (q m n )+ q ×n t, 7 = (3 n)+ 3 n t ( n t)
n = 2 t= 0.
l* (13)
l* = [(q m n) × m + (q ×n t)(m+1)]/ r
l* = ((3-2) 1 + (32 0) (1+1)) / 7 = 13/7 = 1,86.