Friday, 25 August 2017

finite fields - Factorization of x8x over F2 and F4



How can I factorize x8x over the fields F2 and F4?


Answer



Hint: We have that x8x splits as
x(x+1)(x3+x2+1)(x3+x+1)
over F2 and gcd(x8x,x4x)=x2+x=x(x+1).


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