Spearman Permutation Distances and Shannon's Distinguishability

Spearman distance is a permutation distance which might prove useful for coding, e.g. for codes on permutations. It turns out, however, that the Spearman geometry of strings is rather unruly from the point of view of error correction and error detection, and special care has to be taken to discriminate between the two notions of codeword distance and codeword distinguishability. All of this stresses the importance of rejuvenating the latter notion, extending it from Shannon's zero-error information theory to the more general setting of metric string distances.