Sum-free sets in vector spaces over \(GF(2)\)
Let \(V(n)\) denote the standard \(n\)-dimensional vector space of \(n\)-tuples over the field \(GF(2)\). A subset \(S\) of \(V(n)\) is sum-free if \((S+S)\cap S=\emptyset\); for example, the set of all vectors with an odd number of components equal to 1 is a sum-free subset of largest size, namely \(2^{n-1}\). The authors show that any sum-free subset of size less than \(2^{n-1}\) has size at most \(5\times 2^{n-4}\) and find bounds for the size of the smallest maximal sum-free subsets. By constructing various classes of sum-free subsets they are able to give a complete list of the maximal sum-free subsets of \(V(n)\) for \(n\leq 6\) and partial information for \(n>6\).
scientific article; zbMATH DE number 96574