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I have 2 questions.

Finding generators in GF(19) is similar to finding generators in GF(2^p)?

Is primitive polynomial needed to find generators for GF(19)?

Thanks a lot.

Ya Ali.

Mohammad Reza Ramezani
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  • You mean a generator of the multiplicative group? – Hagen von Eitzen Nov 21 '14 at 18:48
  • Is this the prime field of characteristic $;19;$ ? – Timbuc Nov 21 '14 at 18:49
  • Finding generators is relatively similar. In your case the multiplicative group is cyclic of order 18, so you need to exclude elements that have order a proper factor of 18. If an element does not satisfy either of the equations $x^6=1$, $x^9=1$, it is primitive (here $6$ and $9$ were gotten by dividing $18$ by all its prime factors). A primitive polynomial is not needed for a prime field. But IIRC e.g. Matlab uses one. It is IMHO a bit silly, but I guess they have a reason. – Jyrki Lahtonen Nov 21 '14 at 18:56
  • Thanks MR Lahtonen, I still have trouble to find generators in prime field. – Mohammad Reza Ramezani Nov 21 '14 at 19:21

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