Concerning multiplier automorphisms of cyclic Steiner triple systems

Charles J. Colbourn, Eric Mendelsohn, Cheryl E. Praeger, Vladimir D. Tonchev

Research output: Contribution to journalArticle

Abstract

A cyclic Steiner triple system, presented additively over Zv as a set B of starter blocks, has a non-trivial multiplier automorphism λ ≠ 1 when λB is a set of starter blocks for the same Steiner triple system. When does a cyclic Steiner triple system of order v having a nontrivial multiplier automorphism exist? Constructions are developed for such systems; of most interest, a novel extension of Netto's classical construction for prime orders congruent to 1 (mod 6) to prime powers is proved. Nonexistence results are then established, particularly in the cases when v = (2β + 1)α, when v = 9 p with p ≡ 5 (mod 6), and in certain cases when all prime divisors are congruent to 5 (mod 6). Finally, a complete solution is given for all v < 1000, in which the remaining cases are produced by simple computations.

Original languageEnglish (US)
Pages (from-to)237-251
Number of pages15
JournalDesigns, Codes and Cryptography
Volume2
Issue number3
DOIs
StatePublished - Sep 1 1992
Externally publishedYes

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ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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