| Project/Area Number |
14540100
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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 | University of Tsukuba |
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Principal Investigator |
MIAO Ying University of Tsukuba, Graduate School of Systems and Information Engineering, Assistant Professor, 大学院・システム情報工学研究科, 講師 (10302382)
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| Co-Investigator(Kenkyū-buntansha) |
FUJI-HARA Ryoh University of Tsukuba, Graduate School of Systems and Information Engineering, Full Professor, 大学院・システム情報工学研究科, 教授 (30165443)
MISHIMA Miwako Gifu University, Information and Multimedia Center, Associate Professor, 総合情報メディアセンター, 助教授 (00283284)
SHINOHARA Satoshi Meisei University, Faculty of Informatics, Assistant Professor, 情報学部経営情報学科, 講師 (70439694)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Combinatorial Design / Optical Orthogonal Code / Construction / Difference Packing / Finite Geometry / Frequency Hopping Sequence / Information Communication / Information Security / 認証符号 / 閾値秘密分散法 / 電子署名 / 代理暗号系 / 組合せ的デザイン理論 / Incomplete Difference Matrix / 再帰的構成法 / Skew Starter / 有限射影幾何 / Combinatorial design / Optical orthogonal code / code division multiple access / difference packilig / threshold scheme / Projective geometry / difference family / balanced array |
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| Research Abstract |
Optical orthogonal codes are used in optical code-division multi-access communications so that multiple users can efficiently transmit and receive information in one single optic channel. It is known that an optimal optical orthogonal code is equivalent to a combinatorial structure called maximal cyclic t-difference packing. The main purpose of this research project is to construct optimal optical orthogonal codes from a combinatorial approach, that is, instead of constructing optimal optical orthogonal codes directly, we construct their corresponding maximal cyclic t-difference packings.
Fuji-Hara, Miao and Mishima introduced a new concept of incomplete cyclic difference matrices, and used them to construct many cyclic t-difference packings with maximal number of blocks. Together with a computer search, many infinite families of optimal optical orthogonal codes were constructed. The existence of optimal optical orthogonal codes with weight 4, correlation constraint 1, and code length v
… More
with v=0 mod 24 was completely settled.
Shinohara used special arcs and conies in finite geometries to construct optical orthogonal codes and obtained infinite families of asymptotic optimal optical orthogonal codes.
Frequency hopping sequences are used in multi-access spread-spectrum communications which are closely related to optical orthogonal codes. Fuji-Hara, Miao and Mishima found an equivalence relationship between frequency hopping sequences and partition-type difference packings. By using this equivalence, Fuji-Hara, Miao and Mishima constructed many infinite families of optimal frequency hopping sequences.
Miao also considered the security of multi-access communication systems. Topics covered include authentication codes, secret sharing schemes, ID-based signature schemes, and proxy cryptosystems.
Fuji-Hara, Miao, Mishima and Shinohara also carried out theoretical research on several topics in combinatorial design theory which are related to optical orthogonal codes and frequency hopping sequences. Less
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