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I'm wondering if there is any general method I can use to generate reference values other than using these lookup tables mentioned in the following link.

https://www.chegg.com/homework-help/questions-and-answers/develop-set-tables-similar-table-53-textbook-gf-4-modulo-x2-x-1--determine-multiplicative--q16622093

vijitha isuru
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    Whenever I wrote a computer programs to do stuff with finite fields (characteristic two only in my case) I always started out by generating look-up-tables of discrete logarithms (and the inverse table). You can use those to do both addition and multiplication like here. You use discrete logarithms just like the usual logs, but must remember that they are defined modulo $q-1$. – Jyrki Lahtonen Jul 04 '18 at 15:53

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