Question
5.10 Develop a set of tables similar to Table 5.3 for GF(4) with m(x)=x2+x+1.m(x)=x2+x+1. Table 5.3Polynomial Arithmetic Modulo ( x 3 + x + 1
5.10 Develop a set of tables similar to Table 5.3 for GF(4) with m(x)=x2+x+1.m(x)=x2+x+1.
Calculate | Which Satisfies | Calculate | Which Satisifes |
---|---|---|---|
r1(x)=a(x) | v1(x)=1;w1(x)=0 | a(x)=a(x)v1(x)+bw1(x) | |
r0(x)=b(x) | v0(x)=0;w0(x)=1 | b(x)=a(x)v0(x)+b(x)w0(x) | |
r1(x)=a(x) mod b(x)r1(x)=a(x) mod b(x) q1(x)=quotient of a(x)/b(x) | a(x)=q1(x)b(x)+r1(x) | v1(x)=v1(xq1(x)v0(x)=1v1(x)=v1(xq1(x)v0(x)=1 w1(x)=w1(x)q1(x)w0(x)=q1(x) | r1(x)=a(x)v1(x)+b(x)w1(x) |
r2(x)=b(x) mod r1(x) q2(x)=quotient of b(x)/r1(x) | b(x)=q2(x)r1(x)+r2(x) | v2(x)=v0(x)q2(x)v1(x) w2(x)=w0(x)q2(x)w1(x) | r2(x)=a(x)v2(x)+b(x)w2(x) |
r3(x)=r1(x) mod r2(x) q3(x)=quotient of r1(x)/r2(x) | r1(x)=q3(x)r2(x)+r3(x) | v3(x)=v1(x)q3(x)v2(x) w3(x)=w1(x)q3(x)w2(x) | r3(x)=a(x)v3(x)+b(x)w3(x) |
rn(x)=rn2(x) mod rn1(x)rn(x)=rn2(x) mod rn1(x) qn(x)=quotient of rn2(x)/rn2(x) | rn2(x)=qn(x)rn1(x)+rn(x) | vn(x)=vn2(xqn(x)vn1(x)vn(x)=vn2(xqn(x)vn1(x) wn(x)=wn2(x)qn(x)wn1(x) | rn(x)=a(x)vn(x)+b(x)wn(x) |
rn+1(x)=rn1(x) mod rn(x)=0rn+1(x)=rn1(x) mod rn(x)=0 qn+1(x)=quotient of rn1(x)/rn(x) | rn1(x)=qn+1(x)rn(x)+0 | d(x)=gcd(a(x), b(x))=rn(x)d(x)=gcd(a(x), b(x))=rn(x) v(x)=vn(x);w(x)=wn(x) | |
5.11 Determine the multiplicative inverse of x3+x+1x3+x+1 in GF(24)GF(24) with m(x)=x4+x+1.
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