| 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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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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 / 有限体 / ガロア環 / 相対ガウス和 / ガウス和 / 平方剰余型差集合 |
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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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