Abstract
It is proved that a quasi-symmetric design with theSymmetric Difference Property (SDP) is uniquely embeddable as a derived or a residual design into a symmetric SDP design. Alternatively, any quasi-symmetric SDP design is characterized as the design formed by the minimum weight vectors in a binary code spanned by the simplex code and the incidence vector of a point set in PG(2m-1, 2) that intersects every hyperplane in one of two prescribed numbers of points. Applications of these results for the classification of point sets in PG(2m-1, 2) with the same intersection properties as an elliptic or a hyperbolic quadric, as well as the classification of codes achieving the Grey-Rankin bound are discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
