Constructions of Distance-Almost-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 increase the Hamming distance except the original Hamming distance is maximal (equal to the vector length) are useful for the construction of permutation codes. In this paper we propose recursive and explicit constructions of such mappings of length greater than 3 but not equal to 7. Some comparisons show that the new mappings have better distributions of distance increasing than other known distance-preserving mappings (DPMs). We also give some examples to illustrate the applications of these mappings to the constructions of permutation arrays (PAs).