Author: Sven Reichard
Date: 06:40:40 12/10/01
Go up one level in this thread
On December 09, 2001 at 06:57:28, David Rasmussen wrote: >On December 08, 2001 at 12:25:59, Sven Reichard wrote: > >>b) We especially don't want that to happen close to the root. > >Well, sure, but for me it is unacceptable to have it happening at all, if it >means a collision (which it might not necesarily). You can't avoid collisions once you search more nodes than your ttable has entries. >>f) The Hamming distance does depend on the choice of the vector space base. > >I disagree, but maybe I don't understand what you mean. Hamming distance does >not depend on the choice of the vector space base. See the example I gave before (in 2 dimensions). The Hamming distances of a set of vectors changes if you apply a linear transformation. >>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). > >You lost me there. Give me a set of vectors. I pick 64 linearly independent elements from that set (provided that the set spans the whole space) and pick those as the basis vectors. I then express every vector in the set in terms of that basis. That is, the 64 vectors I picked are represented as 0-1 vectors which contain exactly one 1 and 63 0's. Hence, they have weight 1, and their pairwise Hamming distance is two. Thus, my set has minimal weight 1, minimal distance <= 2, and is as good as yours. I'll try and write a program which checks Hamming distance and linear independence for a small dimension. (I don't know if an exhaustive search is feasible.) I'll let you know if I find anything. Sven. Sven
This page took 0.01 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.