In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF(5)^13, with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V, which can also be characterized as the intersections of B with thirteen linear hyperplanes of V.
Pavone, M. (2021). An algebraic representation of Steiner triple systems of order 13. EXAMPLES AND COUNTEREXAMPLES, 1, 100013 [10.1016/j.exco.2021.100013].
An algebraic representation of Steiner triple systems of order 13
Pavone, Marco
Primo
2021-07-06
Abstract
In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF(5)^13, with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V, which can also be characterized as the intersections of B with thirteen linear hyperplanes of V.
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