The Largest Cap in AG(4, 4) and Its Uniqueness
نویسندگان
چکیده
We show that 40 is the maximum number of points of a cap in AG(4, 4). Up to semi-linear transformations there is only one such 40-cap. Its group of automorphisms is a semidirect product of an elementary abelian group of order 16 and the alternating group A5.
منابع مشابه
Partitions of AG(4, 3) into maximal caps
In a geometry, a maximal cap is a collection of points of largest size no three of which are collinear. In AG(4, 3), maximal caps contain 20 points; the 81 points of AG(4, 3) can be partitioned into 4 mutually disjoint maximal caps together with a single point P , where every pair of points that makes a line with P lies entirely inside one of those caps. The caps in a partition can be paired up...
متن کاملA New Division of the Human Claustrum Basis on the Anatomical Landmarks and Morphological Findings
Purpose: The subdivision of claustrum into parts in some species exists in literature. Those are mainly based on a pattern of its connections with various cortical areas, method of staining, immunoreactivity of its neurons etc. The aim of this study was the division of the human claustrum into different parts, for first time, based on morphology, density, arrangement of claustral neurons as wel...
متن کاملThe Classification of the Largest Caps in AG(5, 3)
We prove that 45 is the size of the largest caps in AG(5, 3), and such a 45-cap is always obtained from the 56-cap in PG(5, 3) by deleting an 11-hyperplane.
متن کاملCaps and Colouring Steiner Triple Systems
Hill [6] showed that the largest cap in PG(5, 3) has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 in AG(5, 3). Here we show that the size of a cap in AG(5, 3) is bounded above by 48. We also give an example of three disjoint 45-caps in AG(5, 3). Using these two results we are able to prove that the Steiner triple system AG(5, 3) is 6-chromatic, and so we exhibi...
متن کاملGeneralized Pellegrino caps
A cap in a projective or affine geometry is a set of points with the property that no line meets the set in more than two points. Barwick, et al. (Conics and caps. J. Geom., 100:15–28, 2011) provide a construction of caps in PG(4, q) by “lifting” arbitrary caps of PG(2, q2), such as conics. In this article, we extend this construction by considering when the union of two or more conics in AG(2,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Des. Codes Cryptography
دوره 29 شماره
صفحات -
تاریخ انتشار 2003