Covering arrays from cyclotomy

Designs, Codes, and Cryptography

Volumn 55, Issue 2-3, 2010, Pages 201-219

  Colbourn, Charles J ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

biased array; Covering array; Cyclotomic class; Orthogonal array

Indexed keywords

COVERING ARRAYS; CYCLOTOMIC CLASS; CYCLOTOMY; DISCRETE LOGARITHMS; MATRIX; ORTHOGONAL ARRAY;

ALGEBRA;

MATRIX ALGEBRA;

EID: 77951207016     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-009-9333-8     Document Type: Article

References (24)

1. W. Ananchuen L. Caccetta 1993 On the adjacency properties of Paley graphs Networks 23 4 227 236 0777.05095 10.1002/net.3230230404 1232313
2. J. Azar R. Motwani J. Naor 1998 Approximating probability distributions using small sample spaces Combinatorica 18 151 171 0917.60014 10.1007/PL00009813 1656537 (Pubitemid 128341488)
3. A. Blass G. Exoo F. Harary 1981 Paley graphs satisfy all first-order adjacency axioms J. Graph Theory 5 4 435 439 0472.05058 10.1002/jgt.3190050414 635707
4. Bollobás B.: Random Graphs. Academic Press Inc., London (1985).
5. M.A. Chateauneuf D.L. Kreher 2002 On the state of strength-three covering arrays J. Combin. Des. 10 4 217 238 1003.05022 10.1002/jcd.10002 1905540
6. M.B. Cohen C.J. Colbourn A.C.H. Ling 2008 Constructing strength three covering arrays with augmented annealing Discrete Math. 308 2709 2722 1149.05012 10.1016/j.disc.2006.06.036 2413969 (Pubitemid 351474499)
7. C.J. Colbourn 2004 Combinatorial aspects of covering arrays Le Matematiche (Catania) 58 121 167
8. Colbourn C.J.: Covering array tables. http://www.public.asu.edu/~ccolbou/ src/tabby, 2005-present.
9. Colbourn C.J.: Distributing hash families and covering arrays. J. Combin. Inf. Syst. Sci. (to appear).
10. C.J. Colbourn G. Kéri 2009 Covering arrays and existentially closed graphs Lect. Notes Comput. Sci. 5557 22 33 10.1007/978-3-642-01877-0-3
11. C.J. Colbourn S.S. Martirosyan T. van Trung R.A. Walker II 2006 Roux-type constructions for covering arrays of strengths three and four Des. Codes Cryptogr. 41 33 57 1182.05026 10.1007/s10623-006-0020-8 2253254 (Pubitemid 44343158)
12. M. Forbes J. Lawrence Y. Lei R.N. Kacker D.R. Kuhn 2008 Refining the in-parameter-order strategy for constructing covering arrays J. Res. Nat. Inst. Stand. Tech. 113 5 287 297
13. Godbole A.P. D.E. Skipper Sunley R.A. 1996 t-covering arrays: upper bounds and Poisson approximations Comb. Probab. Comput. 5 105 118 0865.60008 10.1017/S0963548300001905 (Pubitemid 126094311)
14. R.L. Graham J.H. Spencer 1971 A constructive solution to a tournament problem Canad. Math. Bull. 14 45 48 0209.55804 292715
15. Hartman A.: Software and hardware testing using combinatorial covering suites. In: Golumbic M.C., Hartman I. B.-A. (eds.) Interdisciplinary Applications of Graph Theory, Combinatorics, and Algorithms, pp. 237-266. Springer, Norwell, MA (2005).
16. Hedayat A.S., Sloane N.J.A., Stufken J.: Orthogonal Arrays. Springer, New York (1999)
17. G. Katona 1973 Two applications (for search theory and truth functions) of Sperner type theorems Periodica Math. 3 19 26 0266.05001 10.1007/BF02018457 335271
18. D. Kleitman J. Spencer 1973 Families of k-independent sets Discrete Math. 6 255 262 0269.05002 10.1016/0012-365X(73)90098-8 323578
19. Lidl R., Niederreiter H.: Finite Fields, 2nd edn. Cambridge University Press, Cambridge (1997)
20. S.S. Martirosyan C.J. Colbourn 2005 Recursive constructions of covering arrays Bayreuth. Math. Schr. 74 266 275 1122.05019 2220252
21. S.S. Martirosyan T. van Trung 2004 On t-covering arrays Des. Codes Cryptogr. 32 1-3 323 339 1046.05020 10.1023/B:DESI.0000029232.40302.6d 2072336
22. P. Nayeri C.J. Colbourn G. Konjevod 2009 Randomized postoptimization of covering arrays Lect. Notes Comput. Sci. 5874 408 419 10.1007/978-3-642-10217-2- 40
23. Schmidt W.M.: Equations over finite fields. An elementary approach. Lecture Notes in Mathematics, vol. 536. Springer, Berlin (1976).
24. G.B. Sherwood S.S. Martirosyan C.J. Colbourn 2006 Covering arrays of higher strength from permutation vectors J. Combin. Des. 14 3 202 213 1092.05010 10.1002/jcd.20067 2214495 (Pubitemid 43670004)