Author: Ricardo Gibert
Date: 01:38:33 02/10/01
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On February 10, 2001 at 04:01:21, David Rasmussen wrote: >On February 09, 2001 at 19:34:03, Ricardo Gibert wrote: >> >>So far the conclusions I've come up with are: >> >>(1) A Key = 0 should be excluded, since positions with a particular piece on a >>particular square will produce the same hash signature as the same position >>without that piece. > >This excludes all linear codes, which is obviously a good thing to do, because a >linear code would mean that c = a xor b will be a codeword if a and b are >codewords. This means that with exactly three xors you could get the codeword >zero. With 800 codewords, this means that there are lots of different ways to >get 0 which would mean that 0 couldn't possible denote just one position. > >>(3) Pairs of keys of the form x and ~x, since 2 such pairs will XOR to zero. > >This criterion can be met by saying that the code should be non-linear. There's >nothing wrong with a high hamming distance in general, as long as we have a >non-linear code. > >>(4) Pairs with a close hamming distance to x and ~x should also be excluded. > >What do you mean by this? Hamming distance is a number, x and ~x are codewords. I should rewrite this as: Pairs of numbers with a large hamming distance with respect to each other should also be excluded. 2 such pairs would XOR together to a number with a small hamming distance with respect to zero. This is probably still an inept explanation, so here is an example with 16 bit numbers: (0000000011111111^1111111100000001)^(0101010101010101^0010101010101010) = 1111111111111110^0111111111111111 = 1000000000000001 > >>(5) A key set with a hamming distance > 21 and < 43 with respect to each other >>*and* to zero should satisfy (1)-(4) above can be quickly produced within the >>program without having to read in a file with the keys. Just use the same random >>number seed. >> > >Sure, but we might be able to do better. > >>I'm trying to find sources on the net to verify these conclusions, but so far no >>luck. What do you think? > >Search for coding theory. Thanks! I'll try it.
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