Dima Pasechnik <d.pasechnik@quicknet.nl> wrote:
+
 rpw3@rigden.engr.sgi.com (Rob Warnock) writes:
 > Dima Pasechnik <d.pasechnik@quicknet.nl> wrote:
 > +
 >  > So I think there are too many (i.e., >1) incompatible ways to
 >  > implement GF(2^k) that are useful for different algorithms
 >  > to have a useful standard implementation.
 > 
 >  What does prevent you from providing conversions from one
 >  representation to another?
 > +
 >
 > Because in some (but not other!) representations, there's a direct
 > correspondence with *external* data, such that a change of GF
 > representation destroys the correspondence.

 I fail to get your point. Any data conversion can in principle destroy
 data's correspondence with external data. If your data are complex
 numbers in Cartesian representation, and you convert them into polar
 coord. representation, you can lose a property that relies on
 "Cartesianness".
+
That's a good example, actually. If your basic application replies
on the ability to do *fast* vector addition, then changing to polar
representation internally can slow the entire application below the
threshold of usefulness. Or similarly, a conversion from Cartesian
to polar and back will probably destroy the truth of "equal?".
But Cartesian & polar are only two distinct representations for points.
When you get into higherorder GF codes, there may be many, *many*
different representations for the "same" GF, of which only one may be
useful in the a certain application, while a *different* one may have
to be chosen in some other applciation.
That's why trying to define a single "standard" GF representation
is doomed. IMHO.
Rob

Rob Warnock, 312510 rpw3@sgi.com
Network Engineering http://reality.sgi.com/rpw3/
Silicon Graphics, Inc. Phone: 6509331673
1600 Amphitheatre Pkwy. PPASELIA
Mountain View, CA 94043