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If I want to generate tables for $01AB\quad 01AB$ for both addition and multiplication, how will it be generated? I am basically confused from this wikipedia example!

I hope someone can clear it up quickly for me.

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Prakash Wadhwani
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    Those table depend on a chosen element of the field (in your case $A$) being a zero of a hand-picked polynomial (you cannot just use any polynomial for the job). It is basically all polynomial algebra with the coefficients of the polynomials being reduced modulo two, and the high powers of `$A$' being reduced by applying information extracted from the fact that $A$ is a zero of that polynomial. In this Q&A I describe how things work in fields $\Bbb{F}8$ and $\Bbb{F}{16}$. I'm sure $\Bbb{F}_4$ has been covered somewhere in here... – Jyrki Lahtonen May 08 '14 at 08:55
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    The field of four elements is discussed at least here. Not sure about that helping you much, if you are unfamiliar with the theory of quotient rings. – Jyrki Lahtonen May 08 '14 at 08:59
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    This answer may be easier to digest. – Jyrki Lahtonen May 08 '14 at 09:03

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