Concerning multiplier automorphisms of cyclic Steiner triple systems
Document Type
Article
Publication Date
9-1992
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 = 9p 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.
Publication Title
Designs, Codes and Cryptography
Recommended Citation
Colbourn, C.,
Mendelsohn, E.,
Praeger, C.,
&
Tonchev, V.
(1992).
Concerning multiplier automorphisms of cyclic Steiner triple systems.
Designs, Codes and Cryptography,
2(3), 237-251.
http://doi.org/10.1007/BF00141968
Retrieved from: https://digitalcommons.mtu.edu/math-fp/171
Publisher's Statement
© Kluwer Academic Publishers 1992. Publisher’s version of record: https://doi.org/10.1007/BF00141968