Geometric Hyperplanes of the Dual Half-Spin Geometry

Abdelsalam Abou Zayda

doi:10.5539/jmr.v3n1p92

Abstract

We will present two types of geometric hyperplanes of the dual half-spin geometry D5,3 , the class of subspaces of kindp⊥ (p is a point in D5,3) and substructures called Shult sets are determined to be hyperplanes of such geometry. Moreoverwe construct a binary constant weight code using the hyperplanes of the geometry.

Highlights

In a certain class of point-line geometries the geometric hyperplanes were classified
In this paper we presented two types of hyperplanes of the dual half-spin geometry D5,3(q) and we constructed a new family of binary constant-weight codes using such hyperplanes
Given a set I, a geometry Γ over I is an ordered triple Γ = (X, ∗, D), where X is a set, D is a partition Xi of X indexed by I, Xi are called components, and ∗ is a symmetric and reflexive relation on X called incidence relation such that: x ∗ y implies that either x and y belong to distinct components of the partition of X or x = y

Summary

Introduction

In a certain class of point-line geometries the geometric hyperplanes were classified. A polar space is a point-line geometry Γ = (P, L) satisfying the Buekenhout-Shult axiom: For each point-line pair (p, l) with p not incident with ; p is collinear with one or all points of l, that is | p⊥ ∩ |= 1 or else p⊥ ⊃ .

Results

Conclusion