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2015-06-08 20:30:15 +0100 commented question Basis of extension

I am interested in finding $n$ elements of $F_{q^n}$ linear-independent over $F_q$, even when $q$ is not prime.

2015-06-07 22:34:22 +0100 asked a question Basis of extension

Assume that $q$ is a power of a prime number. Consider the field extension $F_q \subset F_{q^n}$ . Both fields can be thought as subfields of the algebraic closure of $F_p$, defined with

K=GF(p).algebraic_closure()

The question is: Is it possible to compute a basis of $F_{q^n}$ over $F_{q}$ ? Or at least to have something in the spirit of

K.<x1,...,xn>=GF(q)[]

which can be done when $q$ is prime?