Dima Pasechnik  <d.pasechnik@quicknet.nl> wrote:
+---------------
| bjl@cs.purdue.edu (Bradley J Lucier) writes:
| > 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. For example, in the
GF polynomials used for error-correcting codes, there is a big
distinction between "systematic" codes (those for which a subset
of the encoded bits *are* the unencoded "user" information bits)
and "non-systematic" codes.

In almost all cases, a conversion of a systematic code from one
GF representation to another will destroy the systematic property,
rendering the code useless for its originally-intended purpose.

(Of course, there are *other* purposes -- e.g., crypto -- for
which non-systematic codes are in fact preferable. But that's
another story...)

In short, while in theory all GF(x)s [for some "x"] are "the same",
in practice they really aren't.


-Rob

-----
Rob Warnock, 31-2-510		rpw3@sgi.com
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