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 ) (x3+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.