If your goal is to find the char-poly modulo a small prime, you _can_ use the trace expansion: Just compute over the rationals. Work modulo several larger primes (> matrix size N), reconstruct the rational solution, reduce mod the small prime of interest. Alternatively, you can just work modulo a power of the small prime; I think the exponent need only exceed the degree to which the small prime divides N!. [N/(p-1)]+1 should do. General finite fields look harder: Maybe use (symbolic) algebraic numbers, over the rationals, then reduce the final answer mod the small prime. For example, phi is a root of X^2 = X+1, and A + B phi models GF[2^2] when A and B are taken mod 2. Rich -------------- Quoting Fred lunnon <fred.lunnon@gmail.com>:
At which point, it suddenly becomes obvious that this notion doesn't help in the slightest with modifying Henry's char poly expansion to meet Gene's criticism in finite characteristic.
Ah well --- apologies for a big fat red herring, everybody!
Does Victor have a reference for the BCH decoding material mentioned earlier? I'm intrigued now to know just how this problem can be sorted out properly.
WFL
On 12/5/09, Mike Stay <metaweta@gmail.com> wrote:
On Fri, Dec 4, 2009 at 3:28 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
the domain is \N and the range \F_p. WFL
OK, that makes all the difference in the world.
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
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