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What are some examples of this? Say for $F_{4}$. I know this is a very simple question, but I can't find any info on it.

Edit: Yes, I was thinking of $F_{2}[x]/(x^2+x+1)$. I was confused.

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    Maybe I'm missing something, but isn't it just $ax+by=c$ as usual?2012-02-13
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    @ad423 you just write a normal equation of a line (as anon mentions), but now you replace numbers by polynomials over $\mathbb{F}_4$. That is, every constant is now allowed to be a polynomials and variables vary over polynomials.. The polynomials themselves should have coefficients in $\mathbb{F}_4$.2012-02-13
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    The title says that the field is a polynomial field. I automatically (mis-)read $F_4[x]$ in the question. I don't know which one OP means.2012-02-13
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    @ad423: Thanks for the edit! Makes more sense now!2012-02-14

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