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 higher-order 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, 31-2-510		rpw3@sgi.com
Network Engineering		http://reality.sgi.com/rpw3/
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