Date: Mar 23, 2010 6:30 PM
Author: semenov.p
Subject: How to embed Hamming space to Hilbert one with minimum distortion?

Good day!
Hamming space is trivial linear space under $\mathbb{F}_2$-field. Is
it possible to embed Hamming space $\mathbb{B}^n$ to Hilbert one with
translating linear variety under operations from $\mathbb{F}_2$ to
linear variety under new field (may be $\mathbb{R}$) operations with
some small distortion? This problem arised becuase I have to have a
dot product that unifies a distance and norm (this is false for
Hamming space because of modulo 2 operations).
Thank you very much!