Construction Classification of weighing matrices of low order and its applications

低阶权重矩阵的构造分类及其应用

• 批准号: 11640125
• 负责人: OHMORI Hiroyuki
• 金额: $ 2.24万
• 依托单位: Ehime University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640125/
• 关键词: weighing matrix; semi-biplane; art gallery theorem; Holding and unholding; Fermat-like diophantine equation; orthogonal array; graphical enumeration; ternary linear code; weighing matrix; semi-biplane; Format-like equation; ウェイイング行列; quarterna

(1) Ohmori completed the classification of weighing matrices W (n, 6) of the semi-biplane type. And furthermore, he completed the classification of weighing matrices W (14,9)(in Japanese).(2) Hirata gave another proofs of art gallery theorems and also showed that there are 17 different polyhedrons constructed from a development of a cube.(3) Okamoto gave criteria on certain diophantine equations concerning Fermatlike equation over algebraic number fields.(4) Shirakura discussed the optimality of orthogonal arrays and constructed. Furthermore, he gave the expornential generating function for some graphs.(5) Hamada showed the nonexistence of some quaternary linear codes and a ternary linear code.

(1)Ohmori完成了半双平面型加权矩阵W（n，6）的分类。此外，他完成了加权矩阵W（14，9）的分类（日文）。(2)平田给出了另一个证明画廊定理，并表明，有17个不同的多面体建造的发展一个立方体。(3)Okamoto给出了代数数域上Fermat-like方程的某些丢番图方程的判别准则。(4)白仓讨论了正交表的最优性并构造了。此外，他还给出了某些图的指数生成函数。(5)Hamada证明了一些四元线性码和一个三元线性码的不存在性。

项目成果

Hiroyuki,Ohmori: "Multivariate analysis, design of experiments, and surery sampling"Subir Ghosh. 663 (2000)

Hiroyuki，Ohmori：“多变量分析、实验设计和确定抽样”Subir Ghosh。

Koichi HIRATA: "Holding and unholding"Ehime Suugakkaishi. 40. 14-18 (1999)

平田浩一：《握住与松开》爱媛须贺石。

Toshiaki Okawoto: "Fermat-like diophantine equations"Mem.Fac.Educ.Ehime Univ.Nat.Sci.. 21(1). 1-6 (2000)

Toshiaki Okawoto：“类费马丢番图方程”Mem.Fac.Educ.Ehime Univ.Nat.Sci.. 21(1)。

H.EGUCHI and K.HIRATA: "Alternate proofs of art gallery theorems"Mem.Fac.Educ.Ehime Univ., Nat.Sci.. 19 (2). 17-22 (1999)

H.EGUCHI 和 K.HIRATA：“美术馆定理的替代证明”Mem.Fac.Educ.Ehime Univ.，Nat.Sci.. 19 (2)。

M.Mishima,M.Jimbo,T.Shirakura: "On the optimality of orthogonal arrays in case of correlated errors"Journal of Statistical Planning and Inference. 88. 319-338 (2000)

M.Mishima、M.Jimbo、T.Shirakura：“关于相关误差情况下正交数组的最优性”统计规划与推理杂志。