Distance preserving mappings from ternary vectors to permutations

TL;DR

This paper introduces a new method for creating distance-preserving mappings from ternary vectors to permutations, enhancing the size bounds of permutation arrays for better error correction.

Contribution

It proposes a novel construction of DPMs from ternary vectors that improves lower bounds on permutation array sizes.

Findings

Improved lower bounds on permutation array sizes.

Construction of DPMs from ternary vectors.

Enhanced error correction capabilities.

Abstract

Distance-preserving mappings (DPMs) are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of the same or longer length such that every two distinct vectors are mapped to permutations with the same or even larger Hamming distance than that of the vectors. In this paper, we propose a construction of DPMs from ternary vectors. The constructed DPMs improve the lower bounds on the maximal size of permutation arrays.