Spearman Permutation Distances and Shannon's Distinguishability

Abstract

Spearman distance is a permutation distance which might be used for codes in permutations beside Kendall distance. However, Spearman distance gives rise to a geometry of strings, which is rather unruly from the point of view of error correction and error detection. Special care has to be taken to discriminate between the two notions of codeword distance and codeword distinguishability. 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.