Glasnik Matematicki, Vol. 56, No. 1 (2021), 1-15.

SYMMETRIC 1-DESIGNS FROM PGL₂(Q), FOR Q AN ODD PRIME POWER

Xavier Mbaale and Bernardo Gabriel Rodrigues

School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban 4000, South Africa
e-mail: xavier@aims.ac.za

Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0028, South Africa
e-mail: bernardo.rodrigues@up.ac.za

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 ∩ M^g|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M.

2010 Mathematics Subject Classification.   05E20, 05E30, 94B05

Key words and phrases.   Symmetric designs, linear code, projective general linear group

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

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