Distance-increasing mappings from binary vectors to permutations

Abstract

Mappings from the set of binary vectors of a fixed length to the set of permutations of the same length that strictly increase Hamming distances except when that is obviously not possible are useful for the construction of permutation codes. In this correspondence, we propose recursive and explicit constructions of such mappings. Some comparisons show that the new mappings have better distance expansion distributions than other known distance-preserving mappings (DPMs). We also give some examples to illustrate the applications of these mappings to permutation arrays (PAs).