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

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2 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2003 Oct


ASJC Scopus subject areas

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

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