Mathematica offers the package
FiniteFields, which supports generation of an irreducible polynomial in a finite field:
IrreduciblePolynomial[s,p,d]: gives an irreducible polynomial in the symbol s of degree d over the integers modulo the prime p.
I have two issues with this function:
- The polynomial generated in this way is always fixed. How can I produce various irreducible polynomials?
- The finite field with respect to which the irreducible polynomial is generated is GF(p), which is of prime order. How can I generate irreducible polynomial with respect to GF($p^n$), for $n>1$?
Edit: An example of what I'm seeking is available here: http://theory.cs.uvic.ca/gen/poly.html