Uniquely optimal codes of low complexity are symmetric

TL;DR

This paper predicts that optimal codes in compact metric spaces are symmetric, providing a framework to test these predictions across different spaces.

Contribution

It formulates explicit predictions about the symmetry of optimal codes, linking theoretical predictions with potential empirical validation.

Findings

Predictions about symmetry of optimal codes in compact metric spaces

Framework for testing symmetry predictions in various spaces

Potential implications for code design and analysis

Abstract

We formulate explicit predictions concerning the symmetry of optimal codes in compact metric spaces. This motivates the study of optimal codes in various spaces where these predictions can be tested.