maken83 wrote:
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????
What do you mean?
If you mean trying to find a degree n polynomial
![f\in\mathbb{F}_p[X]](/CBB/latexrender/pictures/d8f18fa175167f28b0bd939253db1fee.png "f\in\mathbb{F}_p[X]")
such that
![\mathbb{F}_{p^n}\cong\dfrac{\mathbb{F}_p[X]}{\langle f\rangle}](/CBB/latexrender/pictures/981c5b5a78a456ac02540dc54a6b8f3d.png "\mathbb{F}_{p^n}\cong\dfrac{\mathbb{F}_p[X]}{\langle f\rangle}")
, then the easiest is probably to use the usual sieve to find an irreducible polynomial of degree n. It doesn't take long to find
![\mathbb{F}_{41^2}\cong\dfrac{\mathbb{F}_{41}[X]}{\langle X^2+3\rangle}](/CBB/latexrender/pictures/4096325898af44b663d00359426c831e.png "\mathbb{F}_{41^2}\cong\dfrac{\mathbb{F}_{41}[X]}{\langle X^2+3\rangle}")
, for example.
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