composite field GF(q^mn) as vector space over GF(q^m)

[Семенов Петр <semenov.pk@gmail.com>]

Hello, all!

 

I have a problem:

1. I have a composite field GF(q^{m*n}) and let A be its element;

2. I want to get the n-dimensional vector over GF(2^m) corresponding to A.

How can I get a minimal/irreducible polynomial f(x) from GF(q^m)[x] to represent GF(q^{m*n})
as GF(q^m)[x]/<f(x)>?
Unfortunately, I found no functions in PARI/GP allowing me to deal with Galois group for 
finite field extensions.

How can I solve my problem?

Thank you!

 

With best regards,

Piotr Semenov