Original scientific paper

https://doi.org/10.3336/gm.56.1.01

Symmetric 1-designs from PGL2(q), for q an odd prime power

Xavier Mbaale ; School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban 4000, South Africa
Bernardo Gabriel Rodrigues orcid.org/0000-0002-1349-0219 ; Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0028, South Africa

Abstract

All non-trivial point and block-primitive 1-(v, k, k) designs 𝓓 that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M.

Keywords

Symmetric designs, linear code, projective general linear group

Hrčak ID:

259297

URI

https://hrcak.srce.hr/259297

Publication date:

24.6.2021.

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