( d/2) ( , ), . , , , .
. , . n k n-k ,
Rk, 0 ∞, , . , , .
, , Q n- , s . ,
(. . 6.2).
, . .
, , . n- 2n,
. d Q . 6.1.
6.1
, , .
, . , .
, , , . .
, , (, ), , . . . , .
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. , . , . 1, , , , 0, . ( , ) , , , . .
. , ( ). , , , .
, . .
. ( , , ). , .
, , . . ( + b = ) ( ∙b=), , .
, .
, :
1. ( ).
2. , b ( ) ( ).
3. Gn , Gn ( ) ( ).
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0, 1.
4. , +(- ) = - + = 0 ( ) ( ).
(- ), -1.
, , , . . ( ) ab = b ( ), .
, , . .
n- , . q (q ), , q.
2. 0, , 1, , :
, .
, . 2 . , 2 .
6.2. , :
, .
, , 2 1101 1110 0011, .
.
, , , . , : 000, 001, 010, 011 .
Gn . Gn, ( 2) Gn , .
, , , . j , , .
Bj .
, , , .
6.3. .
. 6.2.
6.2
6.4. .
, . . 6.3.
6.3
R, ( ), , :
1) R ;
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2) a R b R R ( );
3) , b R a(bc) = (ab)c ( );
4) , b R (b+) = =ab+ (b+c)a = b+ ( ).
ab = b, . .
.
F , , :
1) ;
2) ;
3) , b, ( )
F , , , . .
GF(P), , . , q, , . , q, q , .
, (0) (1). , 0 1, GF (2). :
, n GF (2), n GF(P). , .
Aj, Ai Af = Ai+Aj, Ak (k=1, 2,..., n) k-x , GF(P). n- .
, q, GF(q) q.
. (, , ) (). .
, (, L Ω). , ω Ω a L c L.
F () V (), :
1) V ;
2) ν V F v, V ( );
3) u ν V , d F , ( );
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4) ν , d , (cd)v = c(dv) 1 ν = ν ( ).
, . n GF(P) ( ) i GF(P) :
[ GF(P)].
(. 3, 4) , n- GF(P), .
, GF (2) (. . 0 1). 2. (1) , (0) , 0= (0 0...0).
n GF(P) , (, , ), n- GF(P).
, , .
, n- GF(P).
o GF (2) , n- . .
6.4.
, Q, . . . n- , , , . ( ) 2 .
( , ), k, .
2k-1 k- n . n k 2 .
2k ( ) n- , 2k n- , , n- . .
, .
2n n- 2k n- , . 2n-k 1 . 2 . , , , . , . ( 2) , .
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, .
, , , ().
, .
, , 2 ( ), , . . . , . , . , , .
, n k. , .
, , , n :
n. , ,
, ,
s
, , . , .
.
. . , 15 . . , , , , (n = 7). .
. , , (. 6.4).
6.4
, , .
, , .
. , , 0...001 0...010.
0...011 . , , , 0...011.
0...0100, . 0...0101 0...0100 0...001 , , , 2 , .. 0...0101.
, 0...0110 0...0110.
, , , 0...0111. , i - , i, , , ί- , , . :
0...01001, 0...01010, 0...01100.
0...0111,
, : 0...0110, 0...0101, 0...0011.
, 1000. 0...01001, 0...01010, 0...01100 : 0...01001, 0...01010, 0...01100.
, 01111.
, , ο :
0 010001 0 0110
0 010010 0 01101
0 010100 0 01011
0 011000 0 00111