Energy bounds for codes and designs in Hamming spaces

TL;DR

This paper establishes universal energy bounds for codes and designs in Hamming spaces, extending previous bounds and accommodating various potential functions for a unified theoretical framework.

Contribution

It introduces a generalized approach to bounding the energy of codes and designs, broadening the scope of Levenshtein bounds in Hamming spaces.

Findings

Universal energy bounds applicable to a wide class of potential functions

Unified framework generalizing Levenshtein bounds

Applicable to both codes and designs in Hamming spaces

Abstract

We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be viewed as a generalization of the Levenshtein bounds for maximal codes.