Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T02:59:03.429Z Has data issue: false hasContentIssue false

Incompleteness of (nq + n - q - 2, n)-arcs in finite projective planes of even order

Published online by Cambridge University Press:  24 October 2008

B. J. Wilson
Affiliation:
Department of Mathematica, Chelsea College (University of London).

Extract

1. It was shown by Barlotti (1) that the number k of points on a (k, n)-arc of a finite projective piane of order q

and that if q ≢ 0 (mod n) then for n ≥ 3

.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1982

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)Barlotti, A.Sui {k, n}-archi di un piano lineare finito. Boll. Un. Mat. Ital. 11 (1956), 553556.Google Scholar
(2)Bruck, R. H. and Ryser, H. J.The non-existence of certain finite projective planes. Canad. J. Math. 1 (1949), 8893.CrossRefGoogle Scholar
(3)Denniston, R. H. F.Some maximal arca in finite projective planes. J. Comb. Theory 6 (1969), 217319.Google Scholar
(4)Hall, M., Swift, J. D. and Walker, R. J.Uniqueness of the projective piane of order eight. Math. Tables Aids Comput. 10 (1956), 186194.CrossRefGoogle Scholar
(5)Segre, B.Introduction to Galois Geometries. Atti. Accad. Naz. Lincei Mem. 8 (1967), 133236.Google Scholar
(6)Thas, J. A.Some results concerning {(q + 1) (n – 1), n}-arcs and {(g + 1) (n – 1)+ 1, n}-arcs in finite projective planes of order q. J. Comb. Theory 19 (1975), 228232.CrossRefGoogle Scholar