26.

, . 1960 (Bose), (Chaudhuri) (Hocquengem) , . -- - (BCH codes).

- , , - (Reed, Solomon), .

g(x) k , xj + 1 g(x) j = 2k - 1 j.

, 1 + x2 + x3 : x7 + 1, xj + 1 j < . 1 + x3 + x4 x15 + 1, xj + 1 j < 15.

g(x) -, n, . q , n ^ 2q - 1 q ^ log2(n + 1). , g(x) = (m1 (x),...,md_1 (x)), m1 (x),...,md_1 (x) ,

, ࠠ , . . . , .

, d, n [].

. - n = d = . q = log2 (n + 1) = 4 x4 + x3 + . , 2 4 . 3 x4 + x3 + x2 + x + . ,

g (x) = ^4 + x3 + 1, x4 + x3 + x2 + x + 1) =

= (x4 + x3 + 1)(x4 + x3 + x2 + x + 1) = x8 + x4 + x2 + x + 1.

8, , - (, 1)-. 1OOO1OO a(x) = x4 + 1 a(x) g(x) = x12 + x6 + x5 + x2 + x + 111OO11OOOOO1OO.

[] - n = 2q - d,

q(d - 1)

-2-.

-, , (92, 2)-, , (2Dz , 2)-, 6.

- . , , -, - . - . , , .

► 45

- g(x) 15 7. m1 (x) = 1 + x + x4 . , 3 5 m3 (x) = 1 + x +

x2 + x3 + x4 m5( x) = 1 + x + x2.