Classification of quasi-symmetric 2-(64,24,46) designs of Blokhuis-Haemers type

Dean Crnkovic; Bernardo Rodrigues; Sanja Rukavina; Vladimir D. Tonchev

paper

Classification of quasi-symmetric 2-(64,24,46) designs of Blokhuis-Haemers type

arXiv:1602.05446

Abstract

This paper completes the classification of quasi-symmetric 2- $(64, 24, 46)$ designs of Blokhuis-Haemers type supported by the dual code $C^{⊥}$ of the binary linear code $C$ spanned by the lines of $A G (3, 2^{2})$ initiated in \cite{bgr-vdt}. It is shown that $C^{⊥}$ contains exactly 30,264 nonisomorphic quasi-symmetric 2- $(64, 24, 46)$ designs obtainable from maximal arcs in $A G (2, 2^{2})$ via the Blokhuis-Haemers construction. The related strongly regular graphs are also discussed.

11 pages