→D+→2→→ ●●● m4m5m6 012345678910111213 me 设信息组m=(memsm4) C6=m6 mo me m6 C5=m5 →D→→D2→→ m4m5- c4-m4 C3=m6+m4=C6+C4 m6+m5 C2=m6+m5+m4=C6+cs+c4 m6+m5+m6 C1=m6+m5=C6+c5 m6+m5 me m6+m5 =m5 m5m6 Co=m5+m4=C5+C4 m4 m5+m4 m5+m4 m6+m5 |m6+m5+m4 m6+m4 mam5m6 →D→D→①+D+①+D+
D0 D1 + D2 + D + 3 D0 D1 + D2 + D + 3 D0 D1 + D2 + D + 3 m4m5m6 m4m5 m5m6 m6 m6+m5 m6 m6 m4 m4m5m6 m6 m6 m6+m5 m6+m5+m6 =m5 D0 D1 + D2 + D + 3 m6+m5 m6 m5+m4 m5+m4 m6+m5 m6+m5+m4 m6+m4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 设信息组m = (m6m5m4 ) c6=m6 c5=m5 c4=m4 c3=m6+m4=c6+c4 c2=m6+m5+m4=c6+c5+c4 c1=m6+m5=c6+c5 c0=m5+m4=c5+c4
三、G与H的关系5 X6 X5X4 X3 X2X g1(X)=X6+X3+x2+X=X(x5+x2+x+1) 100|1110 写成多项式 G= 0100111 =XX+1)(x4+x3+x2+1) 00111101 g2(X)=X+x2+X+1=(X+1)x4+x3+x2+1) g1()=x6+x3+x2+xxx+1)(x4+x3+8N三技￥5t3 g2(X)=X5+X2+X+1=(X+1)(X4+X3+xX2+1)=(X+1)93(X) C(x)=m6g(x)+m5g2(x)+m4g3(x)=m6g1(x)+m5g2(x)+m4g3(X) =msX(x+1)g3(X)+m5(X+1)g3+m493(X) =(m6X2+m6x+m5x+m5+m4)g3(X) =m(xg3(x) 所有码字多项式都是g3()的倍式 又因为是系统码c(x)=m(x)xn-k+r(x)=0(modg3(X) (信息位左移nk位加上监督位) r(x)=-m(x)xn-k (mod g3(x)) 除法电路 (见168页)
三、G与H的关系5 G= 1 0 0 | 1 1 1 0 0 1 0 | 0 1 1 1 0 0 1 | 1 1 0 1 写成多项式 g1 (x)=x6+x3+x2+x=x(x5+x2+x+1) =x(x+1)(x4+x3+x2+1) g2 (x)=x5+x2+x+1=(x+1)(x4+x3+x2+1) g3 (x)= x4+x3+x2+1 g1 (x)=x6+x3+x2+x= x(x+1)(x4+x3+x2+1) =x(x+1)g3 (x) g2 (x)=x5+x2+x+1=(x+1)(x4+x3+x2+1) =(x+1)g3 (x) c(x) =m6g1 (x)+m5g2 (x)+m4g3 (x) =m6g1 (x)+m5g2 (x)+m4g3 (x) =m6x(x+1)g3 (x)+m5 (x+1)g3+m4g3 (x) =(m6x 2+m6x+m5x+m5+m4 )g3 (x) =m(x)g3 (x) 所有码字多项式都是g3 (x)的倍式 又因为是系统码c(x)=m(x)xn-k + r(x) 0 (mod g3 (x)) (信息位左移n-k位 加上监督位） r(x) - m(x)xn-k (mod g3 (x)) 除法电路 （见168页） x 6 x 5x 4 x 3 x 2x