(continuing a thread from June 29) I mentioned a half dozen ways of doing GF2 polynomial multiplication. One of them is to represent the polynomial by its value at several places. [Do the multiplication of the values at each place, then recover the polynomial product (or its values) by interpolation.] Gene points out that GF2 has a limited repertoire of places. FTAW offers the fix of removing the problem to GF[2^k]. I'm mentioning here that you can actually remove the problem to Z, and just use ordinary integers to do the problem, then clip the coefficients back down to 0-1 values. Another option is to do the problem with coefficients moved into Mod P or Mod N, or even a collection of Mods. You can even use mod 2+i, or phi, or 1+w (w=cbrt(1)); the last two shade over into GF[2^k]. Rich ---------- To make this work for GF(2), you have to reinterpret them as polynomials over GF(2^k) for some sufficiently large k. Franklin T. Adams-Watters -----Original Message----- From: Eugene Salamin <gene_salamin@yahoo.com> --- "Schroeppel, Richard" <rschroe@sandia.gov> wrote: ...
Another way to represent polynomials is by giving the values at enough points. ...
But for polynomials over GF2, the only possible values are 0 and 1. Gene