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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
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
Hitoshi Kaneta
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan

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
Copyright
Copyright © Cambridge Philosophical Society 1991

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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), 441459.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), 157164.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), 173186.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), 459462.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), 363366.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), 13141319.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