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Math Help - Galois fields

  1. #1
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    Post Galois fields

    Is there any computer program for finding the elements of GF(p^n), because manually this process is quit lengthy. If we want to find the elements of GF(41^2), it will take several hours. Pleas tell me computer program and command to find the elements of GF(p^n). Is there any list of the elements of GF(p^n) available in internet????
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  2. #2
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    Quote Originally Posted by maken83 View Post
    Is there any computer program for finding the elements of GF(p^n), because manually this process is quit lengthy. If we want to find the elements of GF(41^2), it will take several hours. Pleas tell me computer program and command to find the elements of GF(p^n). Is there any list of the elements of GF(p^n) available in internet????

    I wouldn't worry about the elements of GF(p^n) but about irreducible polynomials of degree n over GF(p) . Once you know

    these the elements of GF(p^n) are easy to write down.

    For example, using Gauss' quadratic law we know that x^2-3 is irreducible over GF(41), so the elements

    in GF(41^2) are all the elements of the form a+b\omega , with \omega^2=3\,,\,\,a,b\in GF(41)...pretty easy!

    Tonio
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