Hyperfocused arcs in PG(2,32)
Giorgio Faina, Cristiano Parrettini, Fabio Pasticci
TL;DR
This paper uses computer-aided search to analyze hyperfocused arcs in PG(2,32), establishing the uniqueness of 12-arcs and the non-existence of 14-arcs, while leaving open the existence of 16-arcs.
Contribution
It proves the uniqueness of hyperfocused 12-arcs and the non-existence of hyperfocused 14-arcs in PG(2,32) through computational methods.
Findings
Hyperfocused 12-arcs are unique up to projectivities.
Hyperfocused 14-arcs do not exist in PG(2,32).
The existence of hyperfocused 16-arcs remains unresolved.
Abstract
In PG(2,32) the following two results are proven by a computer aided search. (i) Uniqueness of hyperfocused 12-arcs, up to projectivities; (ii) Non-existence of hyperfocused 14-arcs. The existence problem for hyperfocused 16-arcs remains open.
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Taxonomy
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Coding theory and cryptography