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How to embed Hamming space to Hilbert one with minimum distortion?
Posted:
Mar 23, 2010 6:30 PM


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!



