From: Fred lunnon <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Sat, December 5, 2009 1:32:54 AM Subject: Re: [math-fun] Expansion of charpoly's in terms of traces ? 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
This discussion has been quite useful. It led to this concept. Definition: A polynomial p(x) with rational coefficients is said to be "almost integer" if p(n) is an integer for all integers n. Example: x(x+1)/2. Conjecture: If f is a periodic function from the integers to the integers mod n, then f(k) = p(k) mod n for some almost integer polynomial p. This idea can also be extended to multivariate polynomials. -- Gene