Distance-Increasing Maps of All Length by Simple Mapping Algorithms

TL;DR

This paper introduces simple mapping algorithms that generate distance-increasing maps (DIMs) for all lengths, simplifying the construction process especially for odd lengths, which were previously complex or recursive.

Contribution

The paper presents a unified, simple method for constructing DIMs of all lengths, including odd lengths, avoiding complex or recursive approaches used before.

Findings

DIMs of all lengths are constructed using simple algorithms.

The new methods simplify the creation of permutation arrays.

The approach applies to both even and odd length DIMs.

Abstract

Distance-increasing maps from binary vectors to permutations, namely DIMs, are useful for the construction of permutation arrays. While a simple mapping algorithm defining DIMs of even length is known, existing DIMs of odd length are either recursively constructed by merging shorter DIMs or defined by much complicated mapping algorithms. In this paper, DIMs of all length defined by simple mapping algorithms are presented.