Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-07T21:19:10.020Z Has data issue: false hasContentIssue false

A note on k-3 caps in three-dimensional Galois space

Published online by Cambridge University Press:  24 October 2008

Dennis Bramwell
Affiliation:
University of the West Indies, Mona, Kingston 7, Jamaica

Extract

A k-3 cap in a three-dimensional Galois space, S3,q, is a set of k points, of which some 3, but no 4 are collinear. It is shown in (2) that for q ≥ 4 .

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1979

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. Ial. (3) 11 (1956), 553556.Google Scholar
(2)Bramwell, D. and Wilson, B. J.Cubic caps in three dimensional Galois space. Proc. Royal Irish Acad. Sect A, 73 (1973), 279283.Google Scholar
(3)Cossu, A.Su alcune proprietà dei {k; n}-archi di un piano proiettivo sopra un corpo finito. Rend. Mat. e Appl. 20 (1961), 271277.Google Scholar
(4)Hill, R.Some results concerning linear codes and (k, 3)-caps in 3-dimensional Galois space. Math. proc. Cambridge Philos. Soc. 84 (1978), 191205.CrossRefGoogle Scholar
(5)MacWilliams, F. J.A theorem on the distribution of weights in a systematic code. Bell System Tech. J. 42 (1963), 7994.CrossRefGoogle Scholar
(6)Thas, J. A.Some results concerning {(q + 1) (n − 1); n}-arcs and {(q + 1) (n − 1) + 1; n}-arcs in finite protective planes of order q. J. Combinatorial Theory, Ser A 19 (1975), 228232.CrossRefGoogle Scholar