Hi,

I have not had time to study it in details, but I found this:
http://fragrieu.free.fr/zobrist.pdf

A Group-Theoretic Zobrist Hash Function
Antti Huima
September 19, 2000
Abstract
Zobrist hash functions are hash functions that hash go positions to
fixed-length bit strings. They work so that every intersection i on a go
board is associated with two values Bi and Wi. To hash a position, all
those values of Bi are XORed together that correspond to an intersec-
tion with black stone on it. Similarly, all Wi’s are XORed together for
those intersections that have a white stone. Then the results are XORed
together.
We present a Zobrist hash function with the extra property that if z is
the hash value of a position p, then the values z′ for the positions p′ that
are obtained from p by exchanging the colors, by rotating the position
and my mirroring can be efficiently calculated from z alone. Still, z and
z′ are different.

Rémi
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