25.

, . .

= 0 ... -1 . () = 0 + 1 + + -1 -1. 2, . . 2.

, 10011 = 5 1 + 3 + 4.

,

() = #0 + 01 ----- 9, 00 = 0, = 0.

() () () = ()() = 0 + &1 + + -1 -1 = 0 -1 0 = 0 = 0 , 0 -1 , . . .

. () = 1 + 2 + 3 01011, () = + 3 + 4, () = ()() = +5 + 7,

. . = 01000101.

() ( + ):

 

"00

01

02

■ ^ 0

0

0

0 -

 

0

00

 

" 0-1

0

0

0

 

0

0

00

^ ^ 0-2

0-1

0

0

 

. 0

0

0

 

 

 

0

. . - , - ( + )- .

, (3, 6)- 1+ +3

" 110 10 0' = 0 110 10

001101

: 000 -> 000000; 001 -> 001101; 010 011010; 011 -> 010111; 100 110100; 101 111001; 110 101110; 111 100011. .

, , , .

(,)- 0(). = 0 ... -1 , () = 0 + 1 + + -1-1 0().

, ()0() + () 0() , () 0(). , 0(), , , , 0(), .

, g (x) : , .

, , x3 + x2 + 1 (4, 7)-, .

, g(x), (m, )-, xj +1 j < n, 3.

d , . d = 2. a(x) , a(x)g(x) = b(x) b(x) n. b 2, b(x) = xm + x1 l < m < n. , b(x) = x1 (xm-1 + 1), , xm-1 + 1 g(x), . , d =1, , xm g(x), . , d ^ 3.

x11 + x9 + x7 + x6 + x5 + x + 1 (12, 23)- (Golay) 7.

1971 [20], .

, bo ... bn-2bn-1 bn-1 b0 ... bn-2.

► 43

x7 + x5 + x + 1 0100, 10001101, 11110.

► 44

10000101011111010011111 11000111011110010011111?