### Abstract

Let F be a finite field of characteristic not 2, and S ⊆ F a subset with three elements. Consider the collection S = {S · a + b a, b ∈ F, a ≠ 0}. Then (F, S) is a simple 2-design and the parameter λ of (F, S) is 1, 2, 3 or 6. We find in this paper the full automorphism group of (F, S). Namely, if we put U = { r {0, 1, r} ∈ S} and K the subfield of F generated by U, then the automorphisms of (F, S) are the maps of the form x g(α(x)) + b, x ∈ F, where b ∈ F, α: F → F is a field automorphism fixing U, and g is a linear transformation of F considered as a vector space over K.

Original language | English |
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Pages (from-to) | 400-412 |

Number of pages | 13 |

Journal | Finite Fields and their Applications |

Volume | 9 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2003 Oct |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Engineering(all)
- Applied Mathematics

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## Cite this

Beidar, K. I., Ke, W. F., Liu, C. H., & Wu, W. R. (2003). Automorphism groups of certain simple 2-(q,3,λ) designs constructed from finite fields.

*Finite Fields and their Applications*,*9*(4), 400-412. https://doi.org/10.1016/S1071-5797(03)00013-3