Adelaide Flocks (cyclic q-clan flocks)

Problem: In the paper cited below, the authors develop a recipe for constructing q-clans starting with a special matrix and the action of a collineation in the associated generalized quadrangle. Using this recipe, flocks of a quadratic cone in PG(3,q), with q = 4k, k = 3, 4, 5, 6, 7 and 8 were found. The first two examples were known from computer searches due to Gordon Royle. The recipe requires a search, and computer limitations will prevent further examples from being generated (for the foreseeable future). It is conjectured that these flocks are part of an infinite family. Needed to prove this would be a "canonical" form for the flock.

First Cited: Payne, S.E., Penttila, T., Royle, G.F., "Building a Cyclic q-Clan". [link to reference]

Activity:Currently being worked on by Bill Cherowitzo, Christine O'Keefe and Tim Penttila.

SOLVED: By the above authors in their paper A Unified Construction of Finite Geometries in Characteristic Two (200?). Some details available on the hyperovals web page

Partial Results:

Comments: It is known that there are strong connections between these flocks and the Subiaco flocks.

The term "Adelaide Flock" is the working title for Cherowitzo, O'Keefe and Penttila.


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