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

K. I. Beidar, W. F. Ke, C. H. Liu, W. R. Wu

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)400-412
Number of pages13
JournalFinite Fields and their Applications
Volume9
Issue number4
DOIs
Publication statusPublished - 2003 Oct

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Linear transformations
Subfield
Linear transformation
Vector spaces
Automorphism
Automorphism Group
Vector space
Galois field
Automorphisms
Subset
Design
Form

ASJC Scopus subject areas

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

Cite this

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.

In: Finite Fields and their Applications, Vol. 9, No. 4, 10.2003, p. 400-412.

Research output: Contribution to journalArticle

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