Combinatorial structures and algorithms commonly included in codes and pooling designs for genetic experiments

在本研究项目中，我们通过研究用于混合设计的组合结构和算法与LDPC码的组合结构和算法，阐明了用于遗传实验的编码和混合设计中常见的组合结构和算法。我们开发了一个信任传播算法来检测大量项目中的正项目，并证明了它对我们的正项目检测算法也是有效的。此外，我们还阐明了对我们的算法有用的组合结构的性质。此外，我们还考虑了组合设计在码、信息传输和密码学领域的应用。

In this research project, we elucidate combinatorial structures and algorithms commonly included in codes and pooling designs for genetic experiments by investigating that the combinatorial structure and algorithm for pooling designs are similar to those of LDPC codes. We developed a belief propagation algorithm to detect positive items among large amount of items and showed that it is effective also for our positive detecting algorithm. And, we clarify the property of combinatorial structures which are useful for our algorithm. Moreover, we consider applications of combinatorial designs to the fields of codes, information transmission and cryptography.