Семенов Петр on Sat, 07 Jan 2012 08:46:26 +0100

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

• To: pari-users@pari.math.u-bordeaux1.fr
• Subject: composite field GF(q^mn) as vector space over GF(q^m)
• From: Семенов Петр <semenov.pk@gmail.com>
• Date: Sat, 7 Jan 2012 11:46:21 +0400
• Delivery-date: Sat, 07 Jan 2012 08:46:26 +0100
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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