Could you please provide the steps involved in calculating a multiplication table for GF(8)?
How do i calculate a multiplication table for GF(8)?
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finite-fields
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1At the risk of blowing my own trumpet: a method (particularly suited for computer implementation) is described in the latter half of my answer to [this question](http://math.stackexchange.com/q/76$0$45/11619). – 2012-11-12
1 Answers
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Take an irriducibile polynomial of degree $3$ over the field $\Bbb F_2$ with two elements, e.g. $P(X)=X^3+X+1$. Then you know that $ \Bbb F_8=\Bbb F_2[X]/(P(X)) $ and that its 8 elements are represented by the 8 polynomials of degree $\leq2$. Thus you can construct the multiplication of $\Bbb F_8$ simply by multiplying these polynomials and taking the result modulo $P(X)$.
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0@GerryMyerson yes i think you are correct – 2012-10-22