I am attempting to construct a field containing 625 elements and should be in the form Zn[x] mod f(x).(adsbygoogle = window.adsbygoogle || []).push({});

Factoring 625 leads to 5^4. So I'm guessing my field will be GF(5^4). So in order for me to construct a field with all elements in it, I need f(x) to be some irreducible polynomial mod 5 of degree 4.

How can I go about finding irreducible polynomials? I know I can choose all the polynomials below degree 4 with coefficients mod 5 and attempt to find one without factors, but that would take forever. Is there a quick way to do this or a list of precomputed irreducible polynomials given GF(p^n) where p is prime and n is greater than 1??

Thanks.

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# Irreducible Polynomials p 5 degree 4

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