Steiner forms. (English) Zbl 1413.15048

Hora, Jan

Commentat. Math. Univ. Carol. 57, No. 4, 527-536 (2016).

Summary: A trilinear alternating form on dimension \(n\) can be defined based on a Steiner triple system of order \(n\). We prove some basic properties of these forms and using the radical polynomial we show that for dimensions up to \(15\) nonisomorphic Steiner triple systems provide nonequivalent forms over \(\mathrm{GF}(2)\). Finally, we prove that Steiner triple systems of order \(n\) with different number of subsystems of order \((n-1)/2\) yield nonequivalent forms over \(\mathrm{GF}(2)\).

MSC:

15A69	Multilinear algebra, tensor calculus
15A63	Quadratic and bilinear forms, inner products

Keywords:

trilinear alternating form; Steiner triple system; radical polynomial

Software:

LOOPS