Minimum dimensional Hamming embeddings.

We consider two metrics decoding equivalent if they impose the same minimum distance decoding for every code. It is known that, up to this equivalence, every metric is isometrically embeddable into the Hamming cube. We present an algorithm which for any translation invariant metric gives an upper bound on the minimum dimension of such an embedding. We also give lower and upper bounds for this embedding dimension over the set of all such metrics.