Applications of combinatorial designs to information transmission and DNA library screening

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In this research project, we studied emerging applications of combinatorial designs. The topics treated in this project are applications to DNA library screening, RAID (redundant array of independent disks), optical orthogonal codes, frequency hopping, (t, m, s)-net, and so on. Especially, we found remarkable development in the field of DNA library screening and RAID.(1) Constructions of pooling designs for DNA library screening and its positive detecting algorithms by Bayesian network : In DNA library screening, it is often required to detect clones with positive response for some test among a huge amount of clones. In order to reduce the number of test, pooling experiment is adapted. In this research, we developed the method to construct 2-consecutive positive detectable matrices to detect consecutive positives among linearly ordered clones. Moreover an efficient algorithm to detect positives are proposed which is based on Bayesian network and is related to low density parity check codes (LDPC).(2) Cluttered ordering and erasure resilient codes for RAID : In RAID system, it is pointed out that the order of writing data to RAIDs is important to raise the speed and to reduce the number of check disks to be renewed. In this research, we found efficient cluttered ordering for 2-dimensional parity system of RAIDs by utilizing wrapped rho-labelling. And we obtained constructions of erasure resilient codes generated by the affine spaces.