| Project/Area Number |
11640099
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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 |
FUJI-HARA Ryoh University of Tsukuba, Institute of Policy and Planning Science, Professor, 社会工学系, 教授 (30165443)
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| Co-Investigator(Kenkyū-buntansha) |
KURIKI Shinji Osaka Profecture University, Graduate school of Engineering, Associate Professor, 大学院・工学研究科, 助教授 (00167389)
MIAO Ying Institute of Policy and Planning Science, Assistant Professor, 社会工学系, 講師 (10302382)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | balanced nested design / balanced array / nested design / code divisible multiple access / optical orthogonal code / resolvable design / (t,m,s)-net / finite affine geometry / Frame / 周波数ホッピング多元接続 / 分割型の差詰集合族 / Balanced Array / Optical orthogonal code / BIBD / n-ary design / cyclic design / Resolvable design / 均斉配列 / Balanced n―ary design / 代数曲線 / 有限体 / Conic / Elliptic Curves |
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| Research Abstract |
Combinatorial problems like orthogonal arrays, balanced arrays, BIBD, etc, are important themes in mathematics since 18^<th> century. Recently those mathematical problems are great matter of concern in application areas like wireless communication, DNA testing and Finance. In this project, we have aimed to construct those applicable combinatorial arrays and designs using algebraic curves and varieties on finite projective geometries. In 1999, we constructed balanced arrays from algebraic curves using a property of multiplicity. In 2000, we constructed code for optical fiber communications, called optical orthogonal code. For this construction, many algebraic and geometrical properties are used. We also found a construction of balanced arrays using geometrical varieties of quadratic functions over finite field. In 2001, we continued to construct optical orthogonal code. Furthermore, we found some construction of resolvable designs and nested designs.
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