### Abstract

A cyclic Steiner triple system, presented additively over Z_{v} 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 = (2^{β} + 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 language | English (US) |
---|---|

Pages (from-to) | 237-251 |

Number of pages | 15 |

Journal | Designs, Codes and Cryptography |

Volume | 2 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1992 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Applied Mathematics

### Cite this

*Designs, Codes and Cryptography*,

*2*(3), 237-251. https://doi.org/10.1007/BF00141968