Abstract
Let \(\mathbb{F}^{(2\nu+\delta)}_{q^{2}}\) be a (2ν+δ)-dimensional unitary space of \(\mathbb{F}_{q^{2}}\) , where δ=0 or 1. In this paper we construct a family of inclusion matrices associated with subspaces of \(\mathbb{F}^{(2\nu+\delta)}_{q^{2}}\) , and exhibit its disjunct property. Moreover, we compare the ratio efficiency of this construction with others, and find it smaller under some conditions.
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References
Aigner M (1996) Searching with lies. J Comb Theory Ser A 74:43–56
Balding DJ, Torney DC (1996) Optimal pooling designs with error detection. J Comb Theory Ser A 74:131–140
Du D, Hwang F (2006) Pooling designs and non-adaptive group testing: Important tools for DNA sequencing. World Scientific, Singapore
Du D, Hwang F, Wu W, Znati T (2006) New construction for transversal design. J Comput Biol 13:990–995
D’yachkov AG, Hwang FK, Macula AJ, Vilenkin PA, Weng C (2005) A construction of pooling designs with some happy surprises. J Comput Biol 12:1129–1136
D’yachkov AG, Macula AJ, Vilenkin PA (2007) Nonadaptive group and trivial two-stage group testing with error-correction d e-disjunct inclusion matrices. In: Csiszár I, Katona GOH, Tardos G (eds) Entropy, search, complexity, 1st edn. Springer, Berlin, pp 71–84. ISBN-10: 3540325735; ISBN-13: 978-3540325734
Erdös P, Frankl P, Füredi D (1985) Families of finite sets in which no set is covered by the union of r others. Isr J Math 51:79–89
Huang T, Weng C (2004) Pooling spaces and non-adaptive pooling designs. Discrete Math 282:163–169
Knill E, Bruno WJ, Torney DC (1998) Non-adaptive group testing in the presence of errors. Discrete Appl Math 88:261–290
Macula AJ (1996) A simple construction of d-disjunct matrices with certain constant weights. Discrete Math 162:311–312
Macula AJ (1997) Error-correcting non-adaptive group testing with d e-disjunct matrices. Discrete Appl Math 80:217–222
Ngo HQ (2008) On a hyperplane arrangement problem and tighter analysis of an error-tolerant pooling design, J Comb Optim 15:61–76
Ngo H, Du D (1999) A survey on combinatorial group testing algorithms with applications to DNA library screening. In: Discrete mathematical problems with medical applications, New Brunswick, NJ, 1999. DIMACS series in discrete mathematics and theoretical computer science, vol 55. Am Math Soc, Providence, pp 171–182
Ngo H, Du D (2002) New constructions of non-adaptive and error-tolerance pooling designs. Discrete Math 243:161–170
Wan Z (2002) Geometry of classical groups over finite fields, 2nd edn. Science, Beijing
Zhang G, Sun X, Li B (2007) Error-correcting pooling designs associated with the dual space of unitary space and ratio efficiency comparison, J Comb Optim (in press)
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Guo, J. Pooling designs associated with unitary space and ratio efficiency comparison. J Comb Optim 19, 492–500 (2010). https://doi.org/10.1007/s10878-008-9185-6
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DOI: https://doi.org/10.1007/s10878-008-9185-6