Designs over finite fields by difference methods

摘要

One of the very first results about designs over finite fields, by S. Thomas, is the existence of a cyclic 2-(n, 3, 7) design over F-2 for every integer n coprime with 6. Here, by means of difference methods, we reprove and improve a little bit this result showing that it is true, more generally, for every odd n. In this way, we also find the first infinite family of non-trivial cyclic group divisible designs over F-2. (C) 2019 Elsevier Inc. All rights reserved.