On the number of Steiner triple systems S(2^m-1,3,2) of rank 2^m - m + 2 over GF(2)

TL;DR

This paper determines the exact count of Steiner triple systems with specific parameters and rank over GF(2), advancing combinatorial design theory.

Contribution

It provides the first explicit enumeration of Steiner triple systems of rank 2^m - m + 2 over GF(2).

Findings

Number of such Steiner triple systems is explicitly calculated.

The result advances understanding of combinatorial designs over GF(2).

Provides a foundation for further enumeration of Steiner systems.

Abstract

We obtain the number of different Steiner triple systems S(2^m-1,3,2) of rank 2^m-m+2 over the field GF(2).