Disjoint maximal arcs in projective planes of order 16

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Sigma Mühendislik ve Fen Bilimleri Dergisi
Volume:42 Issue:1
Disjoint maximal arcs in projective planes of order 16

Disjoint maximal arcs in projective planes of order 16

Authors : Mustafa Gezek

Pages : 82-88

View : 27 | Download : 35

Publication Date : 2024-02-27

Article Type : Research Paper

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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