.
-- () , . . n s. n, k r 2. , , , n : h.
n, , . , g(), s , , P(z) h, GF(2 h) (, z GF(2 h)), i (), (i = 1, 2, , 2s) z i g() = (1(),3(), , 2s-1()).
, , , , , .
g(). ( 3).
h ( 3), ().
g() , .
, .
. α= 10011,, , s=3 n . m = 2 ; ; .
, k=5.
2 n=15 k=5, s=3.
h = log16 = 4, , 4.
i=2s-1=5, 3 1(),3(),5().
g() = (1(),3(),5()) = 10011∙11111∙111 = 10100110111 .
r=10, 10, ,
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β =100110111000010 . .
=111110111000010
3, , :
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3, :
3, :
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, 2, 3 :
β = 100110111000010.
, , s n . m (m ≤ s) ; ; .
s = 3 | 1111101 s = 15 | s = 2 | |||
s = 5 | 1001111000 s = 13 | 1111110 s = 2 | |||
1111001110110011 s = 3 | 01100 s = 3 | 0011110 s = 2 | |||
0001101 s = 15 | 11110100111 s = 5 | 0111010 s = 2 | |||
01010111111 s = 5 | 01010 s = 3 | 0011110 s = 2 | |||
00001 s = 3 | 1000001000 s = 13 | 1110000 s = 2 | |||
1101001 s = 15 | 11111 s = 3 | 0001110 s = 2 | |||
0011001110110010 s = 3 | 01010100000 s = 5 | 0010011 s = 2 | |||
1110001 s = 15 | 10101 s = 3 | 1111111 s = 2 | |||
11110 s = 3 | 1000001110110001 s = 3 | 1111110 s = 2 | |||
01010110101 s = 5 | 1111111 s = 15 | 0101010 s = 2 | |||
0001101000 s = 13 | 01011111111 s = 5 | 1100111 s = 2 | |||
0010101 s = 15 | 1101001010110010 s = 3 | 1010000 s = 2 | |||
11001 s = 3 | 0000001 s = 15 | 1000000 s = 2 | |||
11010000111 s = 5 | 1111111000 s = 13 | 0000010 s = 2 | |||
10. . .
11. ; .
12. . . ; .
13. , . .
14. . .
15. , .
16. --.
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1.
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[2] | ||
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2.
[3].
n | K | r | s | n | k | r | s |
3.
GF(2).
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3().
1. .. : . . . . - .: .., 1989. -320.
2. .. . . -.: , 1979
3. .. . . -.: .., 1987
4. .. . -: , 1977
5. .. , , , 1976
6. ., . , . -.:
[1] .
[2] , , 11 +1, 1001 3+1.
[3] : n , k , r , s .