Galois fields

**maken83** · October 24th 2010, 03:13 AM

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????

**tonio** · October 24th 2010, 04:03 AM

Originally Posted by maken83

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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