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一类二元叠加码的卡氏积及其性质 被引量：4

Descartes Product of A Class of Binary Superimposed Codes and Its Properties
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摘要 二元叠加码d-析取矩阵是组合分组测试理论的一个极其重要的数学模型,定义了两个已知d-析取矩阵的卡氏积并证明了它的性质,最后,对这一定义进行了推广. The binary superimposed code d-disjunct matrix is a extremely important mathematical model of combinatorial group testing theory . Defined Descartes product of the two known d-disjunct matrices as a new d-disjunct matrix and proved its Properties. The last, we introduce generalization of this definition.
作者 王少彧 郝英 王少英 邓超公
机构地区 邯郸学院数理学院 张家口职业技术学院基础部
出处 《数学的实践与认识》 北大核心 2015年第13期319-322,共4页 Mathematics in Practice and Theory
基金 张家口市新能源与信息化产业专项课题(12110019B)
关键词 d-析取矩阵 d^e-disjunct矩阵 卡氏积 汉明距离 检错 d-disjunct matrix d%disjunct matrix Descartes product Hamming distance error detecting
分类号 O151.21-4 [理学—基础数学] G642 [文化科学—高等教育学]
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参考文献8

  • 1Kautz W H, Singleton R C. Nonrandom binary superimposed codes [J]. IEEE Trans Inform Theory,1964, 10:363-377.
  • 2Huang Ta-yuan, Weng Chih-wen. A note on decoding of superimposed codes[J]. Journal of combi-natorial optimization, 2003, 7: 381-384.
  • 3Huang Ta-yuan, Weng Chih-wen. Pooling Spaces and Non-adaptive pooling designs [J]. DiscreteMathematics, 2004, 282:163-169.
  • 4Dyachkov A G, Macula A J, Villenkin P A. Nonadaptive and trivial two-stage group testing witherror-correcting de—disjunct matrices [J]. Springer Berlin Heidelberg, 2007, 16:71-83.
  • 5Du Ding-zhu, Hwang F K. Combinatorial group testing and its applications[M]. Word Scientific,Singepore, 2000.
  • 6Du Ding-zhu, Hwang F K. Pooling designs and nonadaptive group testing[M]. Word Scientific,Singepore, 2006.
  • 7赵向会,李莉,张更生.辛空间的排列问题及具有容错能力的pooling设计的紧界[J].数学物理学报（A辑）,2012,32(2):414-423. 被引量：9
  • 8Mahdi Cheraghchi. Noise-resilient group testing: Limitations and constructions [J]. Discrete Ap-plied Mathematics, 2013, 161: 81-95.

二级参考文献19

  • 1Balding D J, Bruno W J, Knill E, Torney D C. A Comparative of Non-adaptive Pooling Design. Genetic Mapping and DNA Sequencing (Minneapolis, MN, 1994). New York: Springer, 1996:133 154.
  • 2Du D Z, Hwang F K. Combinatorial Group Testing and Its Applications (2nd ed). Singapore: World Scientific, 2000.
  • 3Du D Z, Hwang F K. Pooling Designs and Nonadaptive Group Testing: Important Tools for DNA Se- quencing. Singapore: World Scientific, 2006.
  • 4D'yachkov A G, Hwang F K, Macula A J, et al. A construction of pooling designs with some happy surprises. Journal of Computational Biology, 2005, 12:1129-1136.
  • 5Macula A J, Rykov V V, Yekhanin S. Trivial two-stage group testing for complexes using almost disjunct matrices. Discrete Applied Mathematics, 2004, 137:97-107.
  • 6Balding D J, Torney D C. Optimal pooling design with error detection. Journal of Combinatorial Theory (Series A), 1996, 74:131- 140.
  • 7Macula A J. A simple construction of d-disjunct matrices with certain constant weights. Discrete Mathe- matics, 1996, 162:311-312.
  • 8Macula A J. Error-correcting nonadaptive group testing with de-disjunct matrices. Discrete Applied Mathematics, 1997, 80:217-222.
  • 9Knill E, Bruno W J, Torney D C. Non-adaptive group testing in the presence of error. Discrete Applied Mathematics. 1998: 88:261-290.
  • 10Ngo H Q, Du D Z. New constructions of non-adaptive and error-tolerance pooling designs. Discrete Mathematics, 2002, 243:161-170.

共引文献8

同被引文献13

引证文献4

二级引证文献4

数学的实践与认识
2015年 第13期

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