Distance-preserving mappings from binary vectors to permutations

Abstract

Mappings of the set of binary vectors of a fixed length to the set of permutations of the same length are useful for the construction of permutation codes. In this correspondence, several explicit constructions of such mappings preserving or increasing the Hamming distance are given. Some applications are given to illustrate the usefulness (if the construction. In particular, a new lower bound on the maximal size of permutation arrays (PAs) is given.