Consider A(x)=x^{3}+x^{2}+1 and B(x)=x^{2}+x+1 in GF(11). Also, the

Ayaana Buck

Ayaana Buck

Answered question

2021-11-06

Consider A(x)=x3+x2+1 and B(x)=x2+x+1 in GF(11). Also, the irreducible polinomial is given as p(x)=x3+x+1
1) Find A(x)+B(x) (10 pts)
Hint: Use p(x) if the initial result does not fall in GF(11)
2. Find A2(x)B(x) (20 pts)
Hint: Use p(x) if the initial does not fall in GF(11).

Answer & Explanation

SchulzD

SchulzD

Skilled2021-11-07Added 83 answers

Step 1
A(x)=x3+x2+1
b(x)=x2+x+1
andp(x)=x3+x+1
(a)find A(x)+b(x)
A(x)+B(x)=(X3+x{2}+1)+(x2+x+1)=x3+2x2+x+2
A(x)+B(x)=x3+2x2+x+2
=(x3+x+1)+(2x2+1)
A(x)+B(x)=p(x)+(2x2+1)
p(x) it is initial result.
A(x)+B(x)=x3+2x2+x+2
(b).
A2(x)B(x)=?
A(x)=(x3+x2+1)2
A2(x)=(x3+x2+1)(x3+x2+1)=x6+x5+x3+x5+x4+x2+1
A2(x)=x6+2x5+2x3+x4+2x2+1
A2(x)B(x)=(x6+2x5+2x3+x4+2x2+1)(x2+x+1)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?