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 F2for every integer ncoprime 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.

Designs over finite fields by difference methods

Marco Buratti;
2019

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 F2for every integer ncoprime 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.
2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1458209
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