Respuesta :
Answer:
Step-by-step explanation:
hello,
i advice you check the question again if it is GF([tex]2^{4}[/tex]) or GF(24). i believe the question should rather be in this form;
multiplication in GF([tex]2^{4}[/tex]): Compute A(x)B(x) mod P(x) = [tex]x^{4}[/tex] + [tex]x[/tex]+1, where A(x)=[tex]x^{2}[/tex]+1, and B(x)=[tex]x^{3} + x+1[/tex].
i will solve the above question and i believe with this you will be able to solve any related problem.
A(x)B(x)=[tex](x^{2} +1) (x^{3}+x+1) mod (x^{4}+x+1 ) = (x^{5} +x^{3}+x^{2} ) + (x^{3}+x+1 ) mod (x^{4} + x+1 )[/tex]
= [tex]x^{5}+2x^{3} +x^{2} + x + 1 mod(x^{4}+x+1 )[/tex]
=[tex]2x^{2} +1[/tex]
please note that the division by the modulus above we used
[tex]\frac{x^{5}+2x^{3}+x^{2} +1 }{x^{4}+x+1}= x+\frac{2x^{3} +1}{x^{4}+x+1}[/tex]
