Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-19T12:50:12.706Z Has data issue: false hasContentIssue false
  • English
  • Français

On the uniqueness of (q + 1)-arcs of PG (5, q), q = 2h, h ≥ 4

Published online by Cambridge University Press:  24 October 2008

Tatsuya Maruta  and
Hitoshi Kaneta
Tatsuya Maruta
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
Hitoshi Kaneta
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this paper q = 2h with h ≥ 4, and PG(r, q) stands for the r-dimensional projective space over the finite field GF(q) with q elements.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 91 - 94
Copyright
Copyright © Cambridge Philosophical Society 1991

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

REFERENCES

[1]Bruen, A. A., Thas, J. A. and Blokhuis, A.. On M.D.S. codes, arcs in PG(n, q) with q even, and a solution of three fundamental problems of B. Segre. Invent. Math. 92 (1988), 441–459.CrossRefGoogle Scholar
[2]Casse, L. R. A. and Glynn, D. G.. The solution to Beniamino Segre's problem Ir, q, r = 3, q = 2h. Geom. Dedicata 13 (1982), 157–164.CrossRefGoogle Scholar
[3]Casse, L. R. A. and Glynn, D. G.. On the uniqueness of (q + 1)4-arcs of PG(4, q), q = 2h, h ≥ 3. Discrete Math. 48 (1984), 173–186.CrossRefGoogle Scholar
[4]Hirschfeld, J. W. P.. Projective Geometries over Finite Fields (Oxford University Press, 1979).Google Scholar
[5]Hirschfeld, J. W. P.. Finite Projective Spaces of Three Dimensions (Oxford University Press, 1985).Google Scholar
[6]Kaneta, H. and Maruta, T.. An elementary proof and an extension of Thas' theorem on k-arcs. Math. Proc. Cambridge Philos. Soc. 105 (1989), 459–462.CrossRefGoogle Scholar
[7]Kaneta, H. and Maruta, T.. An algebraic geometrical proof of the extendability of q-arcs in PG(3, q) with q even. Simon Stevin 63 (1989), 363–366.Google Scholar
[8]Kaneta, H. and Maruta, T.. A necessary condition for a quartic surface to be irreducible in the case of characteristic two (preprint).Google Scholar
[9]Roth, R. M. and Lempel, A.. On MDS codes via Cauchy matrices. IEEE Trans. Inform. Theory 35 (1989), 1314–1319.CrossRefGoogle Scholar
[10]Storme, L. and Thas, J. A.. M.D.S. codes and arcs in PG(n, q) with q even: an improvement of the bounds of Bruen, Thas and Blokhuis (preprint).Google Scholar