Abstract
A covering array of size N, strength t, degree k and order v, or a CA(N; t, k, v) in short, is an N × k array on v symbols. In every N × t subarray, each t-tuple occurs in at least one row. Covering arrays have been studied for their significant applications to generating software test suites to cover all t-sets of component interactions. In this paper, we present two constructive methods to obtain covering arrays of strength 5 by using difference covering arrays and holey difference matrices with a prescribed property. As a consequence, some new upper bounds on the covering numbers are derived.
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References
Beth T., Jungnickel D., Lenz H.: Design Theory. Cambridge University Press, Cambridge (1999)
Buratti M.: Cyclic designs with block size 4 and related optimal optical orthogonal codes. Des. Codes Cryptogr. 26, 111–125 (2002)
Chang Y., Yin J.: Further results on optimal optical orthogonal codes with weight 4. Discret. Math. 279, 135–151 (2004)
Colbourn C.J.: Combinatorial aspects of covering arrays. Le Matematiche (Catania) 58, 121–167 (2004)
Colbourn C.J.: Strength two covering arrays: existence tables and projection. Discret. Math. 308, 772–786 (2008)
Colbourn C.J.: Covering table for t = 2,3,4,5,6. http://www.public.asu.edu/~ccolbou/src/tabby/catable.html.
Colbourn C.J., Dinitz J.H.: The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton, FL (2007)
Colbourn C.J., Martirosyan S.S., Mullen G.L., Shasha D.E., Sherwood G.B., Yucas J.L.: Products of mixed covering arrays of strength two. J. Comb. Des. 14, 124–138 (2006)
Colbourn C.J., Martirosyan S.S., Trung T.V., Walker R.A. II: Roux-type constructions for covering arrays of strengths three and four. Des. Codes Cryptogr. 41, 33C57 (2006)
Forbes M., Lawrence J., Lei Y., Kacker R.N., Kuhn D.R.: Refining the in-parameter-order strategy for constructing covering arrays. J. Res. Nat. Inst. Stand. Technol. 113, 287C297 (2008)
Hedayat A.S, Slone N.J.A., Stufken J.: Orthogonal Arrays. Springer, New York (1999)
Ji L., Yin J.: Constructions of new orthogonal arrays and covering arrays of strength three. J. Comb. Theory A 117, 236–247 (2010)
Johnson K.A., Entringer R.C.: Largest induced subgraphs of the n-cube that contain no 4-cycles. J. Comb. Theory B 46, 346–355 (1989)
Keranen M.S., Kreher D.L.: Transverse quadruple systems with five holes. J. Comb. Des. 15, 315–340 (2007)
Li Y., Ji L., Yin J.: Covering arrays of strength 3 and 4 from holey difference matrices. Des. Codes Cryptogr. 50, 339–350 (2009)
Nayeri P., Colbourn C.J., Konjevod G.: Randomized Postoptimization of Covering Arrays. Lecture Notes in Computer Science vol. 5874, pp 408–419 (2009).
Sherwood G.B., Martirosyan S.S., Colbourn C.J.: Covering arrays of higher strength from permutation vectors. J. Comb. Des. 14, 202C213 (2006)
Stinson D.R.: Combinatorial Designs: Construction and Analysis. Springer, New York (2004)
Yin J.: Constructions of difference covering arrays. J. Comb. Theory A 104, 327–339 (2003)
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Communicated by K. T. Arasu.
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Ji, L., Li, Y. & Yin, J. Constructions of covering arrays of strength five. Des. Codes Cryptogr. 62, 199–208 (2012). https://doi.org/10.1007/s10623-011-9505-1
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DOI: https://doi.org/10.1007/s10623-011-9505-1