Packing points into a unit cube in higher space

TL;DR

This paper presents a novel method for densely packing points within high-dimensional unit cubes, ensuring a minimum distance of one between points, using extended Hamming codes for dimensions that are powers of two.

Contribution

It introduces a new construction technique leveraging extended Hamming codes for dense point packing in high-dimensional cubes of power-of-two dimensions.

Findings

Achieves dense packings with guaranteed minimum distance of one.

Applicable to high-dimensional cubes where dimensions are powers of two.

Provides a systematic construction method for such packings.

Abstract

In this paper using the concept of the extended Hamming code we give a construction for dense packing of points at distance at least one in such unit cubes which dimension are a power of two.