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n维有限射影空间上d^e——析取矩阵的新构作

New Construction of d^e——Disjunct Matrix from the n-dimensional Projective Space over Finite Field
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摘要 利用n维有限射影空间上的一些性质,构作了组合群验的数学模型de-析取矩阵,并研究了它的参数和Hamming距离. With the properties of the n-dimensional projective Geometry over Finite Field,it is constructed the new group testing model d^e—disjunct matrix,and studied its parameters and Hamming distance.
作者 刘文菡 黄红芳 赵燕冰
机构地区 邯郸学院数理学院 张家口学院初等教育系 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6期311-314,共4页 Mathematics in Practice and Theory
基金 河北省教育科学"十二五"规划课题(13090070) 河北省张家口市科技支撑研究项目(1112025B)
关键词 n维有限射影空间 de-析取矩阵 HAMMING距离 the n-dimensional projective space over finite field d^e—disjunct matrix hamming distance
分类号 O151.21 [理学—基础数学]
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参考文献11

  • 1Dyachkov A G, Rykov V V. A survey of superimposed code theory[J]. Problems of Control Infor- mation Theory, 1983, 12(4): 1-13.
  • 2Huang T Y, Weng C W. Pooling spaces and nonadaptive pooling designs[J]. Discrete Mathematics, 2004 , 282: 163-169.
  • 3Dyachkov A G, Macula A J, Villenkin P A. Noaadaptive and trivial two-stage group testing with error-correcting d -disjunct matrices[J]. Springer Berlin Heidelberg, 2007, 16: 71-83.
  • 4Du D Z, Hwang F K. Pooling designs and nonadaptive group testing[M]. Word Scientific, Singepore, 2006.
  • 5Li Z T, Gao S G, Du H J, et al. Two constructions of new error-correcting poling design from orthogonal spaces over finite field of characteristic 2 [J]. Journal of combinatorial Optimization, 2010, 20(4): 325-334.
  • 6Du D Z, Hwang F K. Combinatorial Group Testing and Its Applications[M]. Word Scientific, Singe- pore, 2000.
  • 7Hung Q N, Du D Z. New constructions of non-adaptive and error-tolerance pooling design[J]. Dis- :rete Mathematics. 2002. 243:161-1170.
  • 8赵燕冰.n维射影几何上可检错的d-disjunct矩阵[J].河北北方学院学报（自然科学版）,2008,24(A03):10-12. 被引量：1
  • 9赵燕冰,黄中升.n阶射影平面上d-disjunct矩阵的构作[J].河北师范大学学报（自然科学版）,2008,32(3):295-296. 被引量：6
  • 10张海燕,高建平.n维有限射影几何上的Pooling设计[J].数学的实践与认识,2012,24(10):265-268. 被引量：1

二级参考文献19

  • 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. Pooling spaces and non-adaptive pooling designs[J]. Discrete Mathematics, 2004, 282:163-169.
  • 3DU Ding-zhu, HWANG F K. Pooling Designs and Nonadaptive Group Testing[M]. Word Scientific, Singepore, 2006.
  • 4HUNG Q. Ngo, DU Ding-zhu. New constructions of non-adaptive and error-tolerance pooling design[J]. Discrete Mathematics, 2002, 243: 161-1170.
  • 5DU Ding-zhu, HWANG F K. Combinatorial Group Testing and its Applications[M]. Word Scientific, Singepore, 2000.
  • 6Kautz W H, Singleton R C. Nonrandom binary superimposed codes[J]. IEEE Trans. Inform. Theory, 1964, 10:363-377.
  • 7HUANG Ta-yuan, WENG Chih-wen. Pooling Spaces and Non-adaptive Pooling Designs[J]. Discrete Mathematics, 2004, 282:163-169.
  • 8DU Ding-zhu, HWANG F K. Pooling Designs and Nonadaptive Group Testing[M]. Word Scientific, Singepore, 2006.
  • 9DU Ding-zhu, HWANG F K. Combinatorial group testing and its applications[M]. Word Scientific, Singepore, 2000.
  • 10YEH H G. d-disjunct Matrices:Bounds and Lovasz Local Lemma [J]. Discrete Mathematics,2002,253:97-107,

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数学的实践与认识
2015年 第6期

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