Mills, D. DR MATH on Sat, 30 Jun 2001 19:55:01 -0400 |
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Building/Working in Finite Field Extensions |
Here is what I am trying to do: (1) Build the finite field GF(p^n) from the prime field GF(p) using a primitive polynomial of degree n over GF(p) (easy enough); (2) Build GF(p^(nm)) from GF(p^n) using a primitive polynomial of degree m over GF(p^n) (not so easy!). I am performing the second task (rather than just build GF(p^(nm)) from GF(p) with a primitive polynomial in GF(p)[x] of degree nm) because I need to manipulate polynomials of degree m over GF(p^n), specifically factor them over GF(p^n) as well as use roots of irreducible polynomials of degree m over GF(p^n). It appears I can't define a root u of such a polynomial as u=Mod(x,<polynomial of degree m over GF(p^n)>) unless said polynomial's coefficients come from GF(p), which will usually not be the case. I'm sure I am missing something obvious here, and would appreciate it if someone could help me see the forest for the trees. :-) Thanks. -Don Mills