Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T01:53:25.666Z Has data issue: false hasContentIssue false
  • English
  • Français

On vectors of weight 16 in the code of a projective plane of order 10

Published online by Cambridge University Press:  14 November 2011

Alan R. Prince
Alan R. Prince
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh, Scotland
Get access Rights & Permissions [Opens in a new window]

Synopsis

The problem of constructing certain 39-line starts for a projective plane of order 10, assuming that there is a vector of weight 16 in the associated binary code, is considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 137 - 146
Copyright
Copyright © Royal Society of Edinburgh 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Anstee, R. P., Hall, M., Jr. and Thompson, J. G.. Planes of order 10 do not have a collineation of order 5. J. Combin. Theory Ser. A 29 (1980), 39–58.CrossRefGoogle Scholar
2Bruen, A. and Fisher, J. C.. Blocking sets, k-arcs and nets of order 10. Adv. in Math. 10 (1973), 317–320.CrossRefGoogle Scholar
3Carter, J. L.. On the existence of a projective plane of order 10 (Ph.D. thesis, Univ. of California, Berkeley, 1974).Google Scholar
4Denniston, R. H. F.. Nonexistence of a certain projective plane. J. Austral. Math. Soc. 10 (1969), 214–218.CrossRefGoogle Scholar
5Hall, M., Jr. Configurations in a plane of order ten. Ann. Discrete Math. 6 (1980), 157–174.CrossRefGoogle Scholar
6MacWilliams, F. J., Sloane, N. J. A. and Thompson, J. G.. On the existence of a projective plane of order 10. J. Combin. Theory Ser. A 14 (1973), 66–78.CrossRefGoogle Scholar
7Thompson, J. G.. Fixed point free involutions and finite projective planes. In Finite Simple Groups II, pp. 321–337 (London: Academic Press, 1980).Google Scholar