2009/10/31 by William Cherowitzo, Cherowitzo, William · 1 citation
Computer Science · Engineering · Mathematics · #51E20 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:51E20
paper · pdf · doi:10.48550/arxiv.0911.0104
arxiv created 2009/10/31 · openalex publication_date 2009/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first in a series of articles devoted to providing a foundation for a theory of flocks of arbitrary cones in PG(3,q). The desire to have such a theory stems from a need to better understand the very significant and applicable special case of flocks of quadratic cones in PG(3,q). Flocks of quadratic cones have connections with several other geometrical objects, including certain types of generalized quadrangles, spreads, translation planes, hyperovals (in even characteristic), ovoids, inversive planes and quasi-fibrations of hyperbolic quadrics. This rich collection of interconnections is the basis for the strong interest in such flocks. Recent work has indicated that some of these connections can be extended to non-quadratic cones, so there is an additional desire to have such a theory.