Author: Ralf Elvsén
Date: 15:28:58 12/08/01
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On December 08, 2001 at 12:25:59, Sven Reichard wrote: >Just a few more comments; sorry I've not been around for a couple of days. > >The idea that "just a couple of bits have to change" to get from one vector to >another is important in error correcting codes, since there we deal with a >symmetric binary channel where during transmission each bit has an equal >probability of being flipped due to noise. Hence in this case, the Hamming >distance is *the* quality criterion if we can decode the received code by >finding the "closest" code word. >However I hope that my data bus does not represent such a channel; i.e., there >is no noise in my system. >About linear independence: If you pick 768 random vectors of length 64, then >they span the whole space with probability close to 1 (I haven't exactly >computed that, and I don't intend to do it.) >About portability of RNG's: As others have pointed out before, the easiest way >to achieve portability is to generate the codes a priori, store them in a file, >and include them in the distribution. Even using only one compiler, the RNG >could be changed in the next version, making your opening book worthless. > >David, could you once more point out which of the following statements you >disagree with? >a) We want to avoid different positions getting the same code. >b) We especially don't want that to happen close to the root. >c) Hence, we want positions that are only a few moves apart to have different >codes. >d) That means that we want small sets of hash codes to be linearly independent. >e) Linear independence isn't affected by linear transformations. >f) The Hamming distance does depend on the choice of the vector space base. >g) Given a set of vectors with minimal weight and minimal distance 17, there is >a linear transformation moving it to a set of minimal weight 1 and minimal >distance 2 (which in terms of linear independence is just as good as the one we >started with). >h) Given all of the above, the Hamming distance appears to be totally unrelated >to the quality of our set. > >As I said before, if your Hamming criterion works better than pure random >numbers, that's fine with me; I would just like to understand the reason why. >Always the inquisitive mind... > >Actually, the problem of hash codes is a little bit more complicated, since we >also want to avoid minor collisions, i.e., different positions occupying the >same spot in the transposition table. Since usually the first 20 bits of the >hash key determine that position, we would like to avoid linear independence >also for small sets of these truncated vectors. Yes, since your first(?) post about the non-invarianve of the Hamming- distance under rotaions I have started to suspect that for some reason the "Hamming-generated" numbers were better in this sense (i.e. better distributed). But it makes no sense why it should be so... Ralf Have you tried applying the >Hamming criterion to these leading bits? > >Enough for today :) >Sven
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