Designs, Codes and Cryptography

, Volume 40, Issue 2, pp 187–190 | Cite as

There are 1239 Steiner Triple Systems STS(31) of 2-rank 27

  • Octavio Páez OsunaEmail author


A computer search over the words of weight 3 in the code of blocks of a classical Steiner triple system (STS) on 31 points is carried out to classify all STS(31) whose incidence matrix has 2-rank equal to 27, one more than the possible minimum of 26. There is a total of 1239 nonisomorphic STS(31) of 2-rank 27.


Steiner triple system of 2-rank 27 Block code of a design Backtracking search with isomorph rejection 

AMS Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Assmuss Jr. EF (1995) On 2-ranks of Steiner triple systems. Electron J Combin 2 Paper R9 1–35Google Scholar
  2. 2.
    Doyen, J, Hubaut, X, Vandensavel, M 1978Ranks of incidence matrices of Steiner triple systemsMath Z163251259zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    McKay BD (1990) NAUTY user’s guide (version 1.5). Technical Report TR-CS90-02. Computer Science Department, Australian National UniversityGoogle Scholar
  4. 4.
    Tonchev, VD 2001A mass formula for steiner triple systems STS(2 n  − 1) of 2-rank 2 n  − nComb Theory Ser A95197208zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Tonchev, VD, Weishaar, RS 1997Steiner triple systems of order 15 and their codesJ Statist Plann Inference58207216zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Departamento de MatemáticasFacultad de Ciencias, UNAMMéxico

Personalised recommendations