A new upper bound for codes with a single Hamming distance

TL;DR

This paper introduces a novel upper bound on the size of code families with a fixed Hamming distance, using linear algebra techniques to improve understanding of code limitations.

Contribution

It presents a new upper bound for codes with a single Hamming distance, applying the linear algebra bound method for the first time in this context.

Findings

Established a tighter upper bound for single-distance code families

Demonstrated the effectiveness of linear algebra methods in coding theory

Provided insights that could influence code design and analysis

Abstract

In this short note we give a new upper bound for the size of a set family with a single Hamming distance. Our proof is an application of the linear algebra bound method.