Abstract
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 F2 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 F2.
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