2012 Fiscal Year Final Research Report
New constructions of Hadamard matrices based on difference familiesand their generalizations
| Project/Area Number |
23840032
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kumamoto University |
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Principal Investigator |
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| Research Collaborator |
YAMADA Mieko 金沢大学, 数物科学系, 教授 (70130226)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 組合せ論 / 応用数学 / 組合せデザイン / アダマール行列 / 差集合族 / 差集合 / 強正則グラフ / アダマール型差集合 |
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| Research Abstract |
The objective of this research project is to propose new constructions of Hadamardmatrices. Hadamard matrices have several applications in the research areas ofCommunications, Statistics, etc. In the past researches, several constructions ofHadamard matrices have been presented based on difference families, which were obtainedfrom difference sets in finite fields. In our research, by generalizing the knownconstructions of difference families using difference sets in finite fields to those incommutative rings, we extended both of the theories of Hadamard matrices and differencefamilies. In particular, by introducing a new concept generalizing ordinary differencefamilies, we found a new infinite series of difference families in Galois rings and anew construction of Hadamard matrices using the new ones. Furthermore, we investigatedthe linkage between Hadamard matrices, Hadamard difference sets, and strongly regulargraphs.
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Research Products
(14 results)
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[Presentation]2011
Author(s)
籾原幸二、Tao Feng、Qing Xiang
Organizer
2011年度応用数学合同研究集会
Place of Presentation
龍谷大学(滋賀)
Year and Date
2011-12-16
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