Sum-free sets and short covering codes (Q2918473)

A sum free set is a subset of an abelian group such that for all \(a,b,c\) in the subset \(a+b \neq c\). A subset of \(\mathbb F_q^3\) is a covering of the ambient space if for every vector in the space there is a vector in the subset such that the Hamming distance between them is less than or equal to 1. A subset \(H\) of \(\mathbb F_q^3\) is a short covering when \(\mathbb F_q \cdot H\) is a covering. The authors outline a recent link between sum free sets and short coverings. They state two extremal problems concerning this connection.