Disjoint maximal arcs in projective planes of order 16

Year 2024, Volume: 42 Issue: 1, 82 - 88, 27.02.2024

Mustafa Gezek

Abstract

This paper provides the results of some computer searches for disjoint maximal (52, 4)-arcs in the known planes of order 16. Thirty-seven new such sets are discovered: four in Johnson plane and thirty-three in Mathon plane, eighteen of which give examples of 104-sets of type (4,8) coming from non-isomorphic pairs of maximal (52, 4)-arcs, providing first examples for such sets. A new lower bound on the number of 104-sets of type (4,8) coming from disjoint maximal (52, 4)-arcs in the known planes of order 16 is obtained. The 104-length binary and ternary linear codes generated by the blocks of 1-designs associated with the known 104-sets of type (4,8) are classified.

Keywords

Disjoint Maximal ARC, Linear Code, Projective Plane

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