Quasi-symmetric designs, codes, quadrics, and hyperplane sections

Authors

Vladimir Tonchev, Michigan Technological UniversityFollow

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.

Publisher's Statement

© Kluwer Academic Publishers 1993. Publisher’s version of record: https://doi.org/10.1007/BF01264073

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