𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Binary caps with many free pairs of points

✍ Scribed by Petr Lisoněk

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
115 KB
Volume
14
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We introduce the following new viewpoint in the study of caps in PG(m,q). The objective is to maximize, among all caps of given cardinality in a given projective space, the number of free pairs of points, which we define as pairs of points not participating in any coplanar quadruple of points of the cap. We survey the known results (which were motivated by an application in statistical experiment design) and then we improve the known lower bound on the number of free pairs of points for q = 2 and the smallest cap sizes for which the maximization problem is non‐trivial. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 490–499, 2006

📜 SIMILAR VOLUMES

Curves with Many Points and Configuratio
Curves with Many Points and Configurations of Hyperplanes over Finite Fields
✍ Ferruh Özbudak; Henning Stichtenoth 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 147 KB

We establish a correspondence between a class of Kummer extensions of the rational function "eld and con"gurations of hyperplanes in an a$ne space. Using this correspondence, we obtain explicit curves over "nite "elds with many rational points. Some of our examples almost attain the OesterleH bound.

Curves of Every Genus with Many Points,
Curves of Every Genus with Many Points, I: Abelian and Toric Families
✍ Andrew Kresch; Joseph L. Wetherell; Michael E. Zieve 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 157 KB

Let N q g denote the maximal number of F q -rational points on any curve of genus g over F q . Ihara (for square q) and Serre (for general q) proved that lim sup g→∞ N q g /g > 0 for any fixed q. Here we prove lim g→∞ N q g = ∞. More precisely, we use abelian covers of P 1 to prove lim inf g→∞ N q g

Curves with Many Points and Multiplicati
Curves with Many Points and Multiplication Complexity in Any Extension of Fq
✍ Stéphane Ballet 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 157 KB

From the existence of algebraic function "elds having some good properties, we obtain some new upper bounds on the bilinear complexity of multiplication in all extensions of the "nite "eld % O , where q is an arbitrary prime power. So we prove that the bilinear complexity of multiplication in the "n

Adsorption-Induced Aggregation of Colloi
Adsorption-Induced Aggregation of Colloidal Particles in Binary Mixtures: Modeling the Pair Free Energy
✍ J.-M. Petit; B.M. Law; D. Beysens 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 209 KB

homogeneous mixture of water and 2,6-lutidine near the Reversible aggregation of charged colloids in binary mixtures phase separation temperature, T cx , of the liquid mixture. This was first observed in 1985 by changing the temperature of the mixture has a lower consolute temperature at T c Å 34ЊC

Solutions With Bifurcation Points For Fr
Solutions With Bifurcation Points For Free Vibration Of Beams: An Analytical Approach
✍ R. Lewandowski 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 316 KB

The amplitude-frequency relationship for beams in large amplitude free vibration at resonance is investigated. The backbone curve related to an internal resonance is considered by using the Galerkin method. The bifurcation points and both primary and secondary branches of the fundamental backbone cu