Author: Sune Fischer
Date: 15:50:45 12/08/01
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On December 08, 2001 at 18:28:58, Ralf Elvsén wrote: >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 Think of it this way, if you have three vectors a, b and c with hamming distances resp. 1, 2 and 4 then this in itself will guarentee they are linear independent and therefore cannot collide. If you optimize for Hamming distance you may get distances 6, 6 and 6 (for example) and then they no longer need to be linear independent and they might collide. It would seem as though a good spread over Hamming distances will also give a high span of the space for each subset of vectors. But then again since this Hamming trick is so widely used, I wouldn't be surprized if the litterature has a proof somewhere that it increases the spanning (like David says). It is hard to prove either way I think, but if I had a hamming optimizer algorithm I wouldn't mind doing a little collision test myself ;) -S.
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