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I have looked at many websites and forums and none were really that helpful. So my question is, is there an easy way such as a formula or pattern that you can create an irreducible polynomial over $GF(2)$ or $GF(3)$. I know that $x^2+x+1$ is an irreducible polynomial over $GF(2)$. But

How can you tell when the polynomial is longer such as $x^5 +x^3 + x^2 +1$ if it is an irreducible polynomial over $GF(2)$ or $GF(3)$.

I get what an irreducible polynomial is but I want an easy way to verify.

Jesse P Francis
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  • Why do you think an easy way should exist? This is about as difficult as testing for prime numbers. See here. I guess it depends what you mean by easy:-) – Jyrki Lahtonen Dec 22 '15 at 06:41
  • @Lucian: Both your links point at questions about reducibility of polynomials in $\Bbb{Z}[x]$, so I fail to see their relevance. – Jyrki Lahtonen Dec 22 '15 at 06:50

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