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 / Buratti, Marco; Nakic, Anamari. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 57:(2019), pp. 128-138. [10.1016/j.ffa.2019.02.006]
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.File allegati a questo prodotto
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