Considering half-spin geometry of type D6,6(F), we investigate the size of substructures of the geometry called blocking sets. We give an upper bound on size of blocking sets.
ليكن لدينا هندسة النصف مغزلية من نوعD6,6(F )، سنتحقق من حجم تركيبات موجودة داخل الهندسة (سنثبت وجودها ونعطي وصفها) والتي تسمى بالمجموعات المغلقة، وكذلك سنقدم حدا اقصى لحجم تلك المجموعة.
We will present two types of geometric hyperplanes of the dual half-spin geometry D5,3 , the class of subspaces of kind p⊥ (p is a point in D5,3) and substructures called Shult sets are determined to be hyperplanes of such geometry. Moreover we construct a binary constant weight code using the hyperplanes of the geometry
Problem statement:The point-line geometry of type D 4,2 was introduced and characterized by many authors such as Shult and Buekenhout and in several researches many of geometries were considered to construct good families of codes and this forced us to present very important substructures in such geometry that are hyperplanes. Approach: We used the isomorphic classical polar space Ω + (8, F) and their combinatorics to construct the hyperplanes and the family of certain codes related to such hyperplanes. Results: We proved that each hyperplane is either the set ∆ 2 (p) which consisted of all points at a distance mostly 2 from a fixed point p or a Grassmann geometry of type A 3,2 and then we presented a new family of non linear binary constant-weight codes.
Conclusion:The hyperplanes of the geometry D 4,2 allow us to discuss further substructures of the geometry such as veldkamp spaces.
Problem statement:The point-line geometry of type D 4,2 was introduced and characterized by many authors such as Shult and Buekenhout and in several researches many of geometries were considered to construct good families of codes and this forced us to present very important substructures in such geometry that are hyperplanes. Approach: We used the isomorphic classical polar space Ω + (8, F) and their combinatorics to construct the hyperplanes and the family of certain codes related to such hyperplanes. Results: We proved that each hyperplane is either the set ∆ 2 (p) which consisted of all points at a distance mostly 2 from a fixed point p or a Grassmann geometry of type A 3,2 and then we presented a new family of non linear binary constant-weight codes.
Conclusion:The hyperplanes of the geometry D 4,2 allow us to discuss further substructures of the geometry such as veldkamp spaces.
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