You must have a different version of MATLAB than I do (2010b). The error message I get is:
??? Error using ==> gf.gf at 66
X must be between 0 and 2^m-1
I get the same error message if I try this:
GenRoots = 16;
gf(GenRoots,4)
The solution is to use mod:
gf(mod(GenRoots,2^4),4)
EDIT: Similarly, in your loop you need
gf(mod(GenRoots,2^4),4).^(PolyPowers+127)
Note that I am creating the gf element first and then taking the power - with such large powers, you'll get an Inf otherwise!
EDIT 2: On my machine, this code does the same thing as your loop but 2000 times faster:
A1 = gf(repmat(mod((2:129)',2^4),1,128),4);
pp = repmat(1:128,128,1)+127;
A1 = A1.^pp;
