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

Published online by Cambridge University Press:  24 October 2008

Dennis Bramwell
Dennis Bramwell
Affiliation:
University of the West Indies, Mona, Kingston 7, Jamaica
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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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 21 - 23
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Barlotti, A.Sui (k, n)-archi di un piano lineare finito. Boll. Un. Mat. Ial. (3) 11 (1956), 553–556.Google Scholar
(2)Bramwell, D. and Wilson, B. J.Cubic caps in three dimensional Galois space. Proc. Royal Irish Acad. Sect A, 73 (1973), 279–283.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), 271–277.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), 191–205.CrossRefGoogle Scholar
(5)MacWilliams, F. J.A theorem on the distribution of weights in a systematic code. Bell System Tech. J. 42 (1963), 79–94.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), 228–232.CrossRefGoogle Scholar