Abstract
As a generalization of d e-disjunct matrices and (w,r;d)-cover-free-families, the notion of (s,l)e-disjunct matrices is introduced for error-correcting pooling designs over complexes (or set pooling designs). We show that (w,r,d)-cover-free-families form a class of (s,l)e-disjunct matrices. Moreover, a decoding algorithm for pooling designs based on (s,l)e-disjunct matrices is considered.
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References
Chen HB, Fu HL, Hwang FK (2008) An upper bound of the number of tests in pooling designs for the error-tolerant complex model. Opt Lett 2:425–431
D’yachkov AG, Rykov VV, Rashad AM (1989) Superimposed distance codes. Probl Control Inf Theory 18:237–250
D’yachkov AG, Vilenkin P, Macula AM, Torney D (2002) Families of finite sets in which no intersection of l sets is covered by the union of s others. J Comb Theory Ser A 99:195–218
Du D-Z, Hwang FK (2006) Pooling designs and nonadaptive group testing. World Scientific, Singapore
Du D-Z, Ngo HQ (2000) A Survey on Combinatorial Group Testing Algorithms with Applications to DNA Library Screening. DIMACS Ser Discrete Math Theor Comput Sci 55:171–182
Huang T, Weng C (2003) A note on decoding of superimposed codes. J Comb Optim 7:383–384
Huang T, Weng C (2004) Pooling spaces and non-adaptive pooling designs. Discrete Math 282:163–169
Huang H, Huang Y, Weng C (2007) More on pooling spaces. Discrete Math. doi:10.1016/j.disc.2007.11.073
Huang T, Wang K, Weng C (2008) Pooling spaces associated with finite geometry. Eur J Comb 29:1483–1491
Kautz W, Singleton R (1964) Nonrandom binary superimposed codes. IEEE Trans Inf Theory 10:363–377
Macula AJ (1997) Error-correcting nonadaptive group testing with d e-disjunct matrices. Discrete Appl Math 80:217–222
Stinson DR, Wei R (2004) Generalized cover-free families. Discrete Math 279:463–477
Torney DC (1999) Sets pooling designs. Ann Comb 3:95–101
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This paper was presented in Algebraic Combinatorics-an international conference, held in Sendai, June 2006, in honor the 60th Birthday of Professor E. Bannai.
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Huang, T., Wang, K. & Weng, CW. A class of error-correcting pooling designs over complexes. J Comb Optim 19, 486–491 (2010). https://doi.org/10.1007/s10878-008-9179-4
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DOI: https://doi.org/10.1007/s10878-008-9179-4