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I need to find cyclotomic cosets depending on $n=7$ and $q=4$ and find the factorization of $x^7-1$ into irreducible factors over $GF(4)$.

Thanks for any advice.

  • 0
    Well, 1 is a root, so that's a start.2012-10-15
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    So I have $(x-1)(x^6+x^5+x^4+x^3+x^2+x+1)$.2012-10-15
  • 0
    Moreover, $x^7-1$ splits completely over $\mathbb{F}_8$, since its factorization in $\mathbb{F}_2$ is $(1+x)(1+x+x^3)(1+x^2+x^3)$. Note that there is no irreducible polynomial over $\mathbb{F}_2$ with degree $2$ that divides $x^7-1$.2012-10-15

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