On asymmetric coverings and covering numbers

Journal of Combinatorial Designs

Volumn 11, Issue 3, 2003, Pages 218-228

  Applegate, David ^a   Rains, E M ^a,b   Sloane, N J A ^a  

^a AT AND T LABS RESEARCH   (United States)

^b CENTER FOR COMMUNICATIONS RESEARCH   (United States)

Author keywords

Covering designs; Covering numbers; Tur n problem

Indexed keywords

EID: 0242552113     PISSN: 10638539     EISSN: 15206610     Source Type: Journal    
DOI: 10.1002/jcd.10022     Document Type: Article

References (19)

1. W. Bosma and J. Cannon, Handbook of Magma Functions, Sydney, May 22, 1995.
2. W. Bosma, J. Cannon, and G. Mathews, Programming with algebraic structures: Design of the Magma language, Proceedings of the 1994 International Symposium on Symbolic and Algebraic Computation, M. Giesbrecht (Editor), Association for Computing Machinery, 1994, pp. 52-57.
3. W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system I: The user language, J Symb Comp 24 (1997), 235-265. (Pubitemid 127167874)
4. A. E. Brouwer, J. B. Shearer, N. J. A. Sloane, and W. D. Smith, A new table of constant weight codes, IEEE Trans Inform Theory, 36 (1990), 1334-1380.
5. D. de Caen, D. L. Kreher, S. P. Radziszowski, and W. H. Mills, On the covering of t-sets with t + 1+-sets: C9; 5; 4+ and C10; 6; 5, Discrete Math, 92 (1991), 65-77.
6. D. de Caen, D. L. Kreher, and J. Wiseman, On constructive upper bounds for the Turán numbers Tn; 2r + 1; 2r, Nineteenth Southern Conference on Combinatorics, Graph Theory, and Computing (Baton Rouge, 1988), Congress Numer 65 (1988), 277-280.
7. J. N. Cooper, R. B. Ellis, and A. B. Kahng, Asymmetric binary covering codes, J Combin Theory, Series A, to appear.
8. CPLEX Manual, CPLEX Organization, Inc., Incline Village, Nevada, 1991.
9. R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, Scientific Press, San Francisco, 1993.
10. G. R. Giraud, Remarques sur deux problèmes extrémaux, Discrete Math 84 (1990), 319-321.
11. D. Gordon, La Jolla Covering Repository, published electronically at http://www. ccrwest.org/cover.html.
12. A. Hartman and K. T. Phelps, Steiner quadruple systems, Contemporary Design Theory, J. H. Dinitz and D. R. Stinson (Editors), Wiley, New York, 1992, pp. 205-240.
13. P. Kaski and P. R. J. Östergard, The Steiner triple systems of order 19, preprint.
14. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.
15. W. H. Mills and R. C. Mullin, Coverings and packings, Contemporary Design Theory: A Collection of Surveys, J. H. Dinitz and D. R. Stinson (Editors), Wiley, New York, 1992, pp. 371-399.
16. K. J. Nurmela and P. R. J. Östergard, New coverings of t-sets with (t + 1)-sets, J Combin Des 7 (1999), 217-226.
17. K. J. Nurmela and P. R. J. Östergard, New coverings of t-sets with (t + 1)-sets: Appendix, published electronically at http://www.tcs.hut.fi/ Publications/papers/table3.html.
18. N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, published electronically at http://www.research.att.com/-njas/sequences.
19. D. R. Stinson, Coverings, The CRC Handbook of Combinatorial Designs, C. J. Colbourn and J. H. Dinitz (Editors), CRC Press, Boca Raton, FL (1996), pp. 260-265.