TY - JOUR
T1 - Covering and radius-covering arrays
T2 - Constructions and classification
AU - Colbourn, Charles
AU - Kéri, G.
AU - Rivas Soriano, P. P.
AU - Schlage-Puchta, J. C.
N1 - Funding Information:
Thanks are due to Tim Penttila for useful comments on finite geometry. Research of the first author is supported by DOD grants N00014-08-1-1069 and N00014-08-1-1070 . Research of the second author is partly supported by OTKA grants K 60480 and K 77420 .
PY - 2010/6/6
Y1 - 2010/6/6
N2 - The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays, explicit constructions from covering codes are developed. Lower bounds are improved upon using connections to orthogonal arrays, partition matrices, and covering codes, and in specific cases by computation. Consequently for some parameter sets the minimum size of a covering array is determined precisely. For some of these, a complete classification of all inequivalent covering arrays is determined, again using computational techniques. Existence tables for up to 10 columns, up to 8 symbols, and all possible strengths are presented to report the best current lower and upper bounds, and classifications of inequivalent arrays.
AB - The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays, explicit constructions from covering codes are developed. Lower bounds are improved upon using connections to orthogonal arrays, partition matrices, and covering codes, and in specific cases by computation. Consequently for some parameter sets the minimum size of a covering array is determined precisely. For some of these, a complete classification of all inequivalent covering arrays is determined, again using computational techniques. Existence tables for up to 10 columns, up to 8 symbols, and all possible strengths are presented to report the best current lower and upper bounds, and classifications of inequivalent arrays.
KW - Classification of codes
KW - Covering array
KW - Partition matrix
KW - Simulated annealing
KW - Surjective code
KW - Symbol fusion
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U2 - 10.1016/j.dam.2010.03.008
DO - 10.1016/j.dam.2010.03.008
M3 - Article
AN - SCOPUS:77951204047
SN - 0166-218X
VL - 158
SP - 1158
EP - 1180
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 11
ER -