(n,k)- U = (U0, U1, ..., Un-1) n . , U0, U1, ..., Un-1 X,

U() = f() = U0 +U1× + U2×2

+...+Un- 1×n-1 . (1.51)

, , n -1, g(x).

g(x)

.

.

GF(2).

f(x)

g(x) GF(2) GF(2),

:

f(x) + g(x) =

. (1.52)

, mod2 .

 

+ X3+X2+0×X+1

X+1


3 + 2 + + 0 = 3 + 2 + X , (1.53)


:

 

X3 + X2 + 0×X + 1

X2 + X + 1


X3 + 0 + X + 0 = X3 + X. (1.54)


 

GF(2) GF(2), :

f(x)× g(x)=

, (1.55)

, 2.