A Small Maximal Sidon Set in ${\mathbb{Z}}_2^n$

Abstract

A Sidon set is a subset of an Abelian group with the property that each sum of two distinct elements is distinct. We construct a small maximal Sidon set of size $O((n \cdot 2^n)^{1/3})$ in the group ${\mathbb{Z}}_2^n$, generalizing a result of Ruzsa concerning maximal Sidon sets in the integers.