The number of the non‐full‐rank Steiner triple systems

The number of the non‐full‐rank Steiner triple systems Full article

Journal

Journal of Combinatorial Designs
ISSN: 1063-8539

Output data

Year: 2019, Volume: 27, Number: 10, Pages: 571-585 Pages count : 15 DOI: 10.1002/jcd.21663

Tags

2‐rank, 3‐rank, Steiner triple system

Authors

Shi M. ¹ , Xu L. ¹ , Krotov D.S. ²

Affiliations

1	Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematics, Anhui University, Hefei, Anhui Province, P.R. China
2	Sobolev Institute of Mathematics, Novosibirsk, Russia

The p-rank of a Steiner triple system (STS) B is the dimension of the linear span of the set of characteristic vectors of blocks of p, over GF(p). We derive a formula for the number of different STSs of order v and given 2-rank r2, r2<v, and a formula for the number of STSs of order v and given 3-rank r3, r3<v-1. Also, we prove that there are no STSs of 2-rank smaller than v and, at the same time, 3-rank smaller than v-1. Our results extend previous study on enumerating STSs according to the rank of their codes, mainly by Tonchev, V.A. Zinoviev, and D.V. Zinoviev for the binary case and by Jungnickel and Tonchev for the ternary case.

Shi M. , Xu L. , Krotov D.S.
The number of the non‐full‐rank Steiner triple systems
Journal of Combinatorial Designs. 2019. V.27. N10. P.571-585. DOI: 10.1002/jcd.21663 WOS Scopus РИНЦ OpenAlex

Published online:

Aug 1, 2019

Web of science:	WOS:000480071100001
Scopus:	2-s2.0-85070091017
Elibrary:	41622880
OpenAlex:	W3103931004

DB	Citing
Web of science	5
Scopus	5
Elibrary	4
OpenAlex	6