Title
Quasi-symmetric designs, codes, quadrics, and hyperplane sections
Document Type
Article
Publication Date
12-1993
Abstract
It is proved that a quasi-symmetric design with the Symmetric 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.
Publication Title
Goemetriae Dedicata
Recommended Citation
Tonchev, V.
(1993).
Quasi-symmetric designs, codes, quadrics, and hyperplane sections.
Goemetriae Dedicata,
48(3), 295-308.
http://doi.org/10.1007/BF01264073
Retrieved from: https://digitalcommons.mtu.edu/math-fp/168
Publisher's Statement
© Kluwer Academic Publishers 1993. Publisher’s version of record: https://doi.org/10.1007/BF01264073