2000 Fiscal Year Final Research Report Summary
Construction Classification of weighing matrices of low order and its applications
| Project/Area Number |
11640125
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehime University |
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Principal Investigator |
OHMORI Hiroyuki Ehime University, Department of Mathematics, Professor, 教育学部, 教授 (20036370)
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| Co-Investigator(Kenkyū-buntansha) |
SHIRAKURA Teruhiro Kobe University, Department of Mathematics, Professor, 発達科学部, 教授 (30033913)
OKAMOTO Toshiaki Ehime University, Faculty of Education, Associated Professor, 教育学部, 助教授 (50036414)
HIRATA Koichi Ehime University, Faculty of Education, Professor, 教育学部, 教授 (80173235)
HAMADA Noboru Osaka Woman University, Faculty of Science, Professor, 理学部, 教授 (90033844)
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| Project Period (FY) |
1999 – 2000
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| Keywords | weighing matrix / semi-biplane / art gallery theorem / Holding and unholding / Fermat-like diophantine equation / orthogonal array / graphical enumeration / ternary linear code |
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| Research Abstract |
(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.
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