Matroids, Quantum Information Theory, and Codes
| Project/Area Number |
26400187
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kumamoto University |
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Principal Investigator |
Keisuke Shiromoto 熊本大学, 大学院先端科学研究部(工), 教授 (00343666)
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| Co-Investigator(Kenkyū-buntansha) |
千葉 周也 熊本大学, 大学院先端科学研究部(工), 講師 (80579764)
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| Co-Investigator(Renkei-kenkyūsha) |
USUDA Tsuyoshi 愛知県立大学, 情報科学部, 教授 (80273308)
CHIGIRA Naoki 熊本大学, 大学院先端科学研究部, 准教授 (40292073)
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| Research Collaborator |
Thomas Britz University of New South Wales, School of Mathematics, Senior Lecturer
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | マトロイド / 量子情報 / 線形符号 / 符号理論 / 量子情報理論 / 組合せ論 |
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| Outline of Final Research Achievements |
In algebraic coding theory, I have studied mainly the existence problem and the construction problem of codes. Based on these problems, I tried to consider a kind of the similar problems in matroid theory and quantum information theory in this research period. The main results contain a classification theorem and an upper bound on critical exponents of any representative matroids over finite fields and a classification result on the critical exponent of a Dowling matroid over a finite field.
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Report
(4 results)
Research Products
(40 results)
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[Presentation] On the covering number of matroids2016
Author(s)
Keisuke Shiromoto
Organizer
The Japanese Conference on Combinatorics and its Applications (JCCA 2016)
Place of Presentation
Kyoto University, Clock Tower Centennial Hall (Kyoto, Japan)
Related Report
Int'l Joint Research
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[Presentation] On the covering number of matroids2016
Author(s)
Keisuke Shiromoto
Organizer
The 40th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (40ACCMCC)
Place of Presentation
University of Newcastle (Newcastle, Australia)
Related Report
Int'l Joint Research
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[Presentation] Critical exponents of Dowling matroids2015
Author(s)
Yoshitaka Koga
Organizer
39th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
Place of Presentation
University of Queensland (Brisbane, Australia)
Year and Date
2015-12-07
Related Report
Int'l Joint Research
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