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On (n, k, l, Δ)-systems

Published online by Cambridge University Press:  20 January 2009

Stephen D. Cohen  and
Nikolai N. Kuzjurin
Stephen D. Cohen
Affiliation:
Department of MathematicsUniversity of GlasgowGlasgow G12 8QW, Scotland
Nikolai N. Kuzjurin
Affiliation:
Institute for Cybernetics ProblemsAcademy of ScienceVavilova 37, Moscow, 117312, Russia
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Abstract

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The paper is devoted to studying one generalization of Steiner systems S(n, k, l) closely related to packings and coverings of l-tuples by k-tuples of an n-set. One necessary and one sufficient condition for the existence of such designs are obtained.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 53 - 62
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Birch, B. J. and Swinnerton-Dyer, H. P. F., Note on a problem of Chowla, Acta Arith. 5 (1959), 417–423.CrossRefGoogle Scholar
2.Cohen, S. D., Uniform distribution of polynomials over finite fields, J. London Math. Soc. 6 (1972), 93–102.CrossRefGoogle Scholar
3.Cohen, S. D., Regular directed graphs with small diameter constructed by polynomial factorization, submitted.Google Scholar
4.Dembowski, P., Finite Geometries (Springer, Berlin 1968).CrossRefGoogle Scholar
5.Effinger, G. W., A Goldbach theorem for polynomials of low degree over odd finite fields, Acta Arith. 42 (1983), 324–365.CrossRefGoogle Scholar
6.Erdos, P. and Spencer, J., Probabilistic methods in combinatorics (Akademi Kiado, Budapest, 1974).Google Scholar
7.Graham, R. L. and Sloane, N. J. A., Lower bounds for equal weight error correcting codes, IEEE Trans. Inform. Theory 26 (1980), 37–43.CrossRefGoogle Scholar
8.Grannell, M. J. and Griggs, T. S., A Steiner System (5, 6, 108), Discrete Math, to appear.Google Scholar
9.Hanani, H., On quadruple systems, Canad. J. Math. 12 (1960), 145–157.CrossRefGoogle Scholar
10.Hanani, H., On some tactical configurations, Canad. J. Math. 15 (1963), 702–722.CrossRefGoogle Scholar
11.Hanani, H., On balanced incomplete block designs and related designs, Discrete Math. 11 (1975), 255–369.CrossRefGoogle Scholar
12.Helleseth, T., On covering radius of cyclic linear codes and arithmetic codes, Discrete Appl. Math. 11 (1985), 157–173.CrossRefGoogle Scholar
13.Ingham, A. E., On the difference between consecutive primes, Quart. J. Oxford 8 (1937), 255–266.CrossRefGoogle Scholar
14.Johnson, S. M., A new upper bound for error-correcting codes, IEEE Trans. Inf. Theory 8 (1962), 203–207.CrossRefGoogle Scholar
15.Kuzjurin, N. N., On some asymptotically optimal packings. Algebraical and combinatorial methods in applied mathematics, Gor'ky (1979), 57–65 (in Russian).Google Scholar
16.Macwilliams, F. J. and Sloane, N. J. A., The theory of error-correcting codes (North-Holland, 1977).Google Scholar
17.Semakov, N. V. and Zinov'ev, V. A., Balanced codes and tactical configurations, Problems Inform. Transmission 5 (3) (1969), 22–28.Google Scholar
18.Tietäväinen, A., On the covering radius of long binary BCH codes, Discrete Appl. Math. 16 (1987), 75–77.CrossRefGoogle Scholar
19.Vladutz, S. G. and Skorobogatov, A. N., Covering radius of long BCH-codes, Problemi peredachi informasii 25 (1989), 38–45 (in Russian).Google Scholar
20.Wilson, R. M., An existence theory for pairwise balanced designs, J. Combin. Theory Ser. A 13 (1972), 220–273.CrossRefGoogle Scholar
21.Wilson, R. M.The necessary conditions for t-designs are sufficient for something, Utilitas Math. 4 (1973), 207–215.Google Scholar
22.Wilson, R. M., An existence theory for pairwise balanced designs: III-Proof of the existence conjectures, J. Combin. Theory Ser. A 18 (1975), 71–79.CrossRefGoogle Scholar