Abstract
We will show that associated with the classical 1-system of the elliptic quadric Q −(7, q) are certain infinite families of two-character sets with respect to hyperplanes, and partial ovoids of Q +(15, q).
Similar content being viewed by others
References
Calderbank R., Kantor W.M.: The geometry of two-weight codes. Bull. London Math. Soc. 18, 97–122 (1986)
Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A.: Atlas of Finite Groups. Oxford University Press, Eynsham (1985)
Cossidente A., King O.H.: Twisted tensor product group embeddings and complete partial ovoids on quadrics in PG(2t−1, q). J. Algebra 273(2), 854–868 (2004)
Cossidente A., King O.H.: Maximal subgroups of finite orthogonal groups stabilizing spreads of lines. Comm. Algebra 34(12), 4291–4309 (2006)
De Winter S., Thas J.A.: On semi-pseudo-ovoids. J. Algebraic Combin. 22(2), 139–149 (2004)
Delsarte Ph.: Weights of linear codes and strongly regular normed spaces. Discrete Math. 3, 47–64 (1972)
Dye R.H.: Partitions and their stabilizers for line complexes and quadrics. Ann. Mat. Pura Appl. 114(4), 173–194 (1977)
Ebert G.L.: Partitioning projective geometries into caps. Canad. J. Math. 37, 1163–1175 (1985)
Kantor W.M., Liebler R.: The rank 3 permutation representations of the finite classical groups. Trans. Amer. Math. Soc. 271, 1–71 (1982)
Luyckx D.: m–systems of finite classical polar spaces. Ph.D. Thesis, Ghent University (2002).
Luyckx D., Thas J.A.: The uniqueness of the 1-system of Q −(7, q), q odd. J. Combin. Theory Ser. A 98(2), 253–267 (2002)
Luyckx D., Thas J.A.: The uniqueness of the 1-system of Q −(7, q), q even. Discrete Math. 294, 133–138 (2005)
Shult E.E., Thas J.A.: m-systems of polar space. J. Combin. Theory Ser. A 68, 184–204 (1994)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Juergen Bierbrauer.
Rights and permissions
About this article
Cite this article
Cossidente, A. The classical 1-system of Q −(7, q) and two-character sets. Des. Codes Cryptogr. 54, 1–9 (2010). https://doi.org/10.1007/s10623-009-9300-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-009-9300-4
Keywords
- Line-spread
- 1-system
- Finite orthogonal group
- Finite symplectic group
- Maximal subgroup
- Two-character set
- Partial ovoid