### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

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

### Cite this

*Finite Fields and their Applications*,

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

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

Research output: Contribution to journal › Article

*Finite Fields and their Applications*, vol. 9, no. 4, pp. 400-412. https://doi.org/10.1016/S1071-5797(03)00013-3

}

TY - JOUR

T1 - Automorphism groups of certain simple 2-(q,3,λ) designs constructed from finite fields

AU - Beidar, K. I.

AU - Ke, W. F.

AU - Liu, C. H.

AU - Wu, W. R.

PY - 2003/10

Y1 - 2003/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0142246435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142246435&partnerID=8YFLogxK

U2 - 10.1016/S1071-5797(03)00013-3

DO - 10.1016/S1071-5797(03)00013-3

M3 - Article

AN - SCOPUS:0142246435

VL - 9

SP - 400

EP - 412

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

IS - 4

ER -