Distance-preserving and distance-increasing mappings from ternary vectors to permutations

Abstract

Permutation arrays have found applications in powerline communication. One construction method for permutation arrays is to map good codes to permutations using a distance-preserving mappings (DPM). DPMs are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of some fixed length (the same or longer) such that every two distinct vectors are mapped to permutations with the same or larger Hamming distance than that of the vectors. A DIM is called distance increasing (DIM) if the distances are strictly increased (except when the two vectors are equal). In this correspondence, we propose constructions of DPMs and DIMs from ternary vectors. The constructed DPMs and DIMs improve many lower bounds on the maximal size of permutation arrays.