A fusion of hyperplane arrangements and error correcting codes
| Project/Area Number |
16K17582
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nagoya Institute of Technology (2018)
Tokyo Denki University (2016-2017) |
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Principal Investigator |
Nakashima Norihiro 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (90732115)
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| Research Collaborator |
Tsujie Shuhei
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 超平面配置 / 誤り訂正符号 / 特性多項式 / Hamming重み多項式 / Coboundary多項式 / Catalan配置 / Shi配置 / 代数学 / 応用数学 / 自由配置 |
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| Outline of Final Research Achievements |
We studied hyperplane arrangements, error correcting codes and their relations. The results are following. (1) We expressed the coboundary polynomial and the extended Hamming weight enumerator of the Catalan arrangements using set partitions. (2) We obtained the exponential generating function of the number of elements in the intersection lattices of the extended Catalan arrangements and the extended Shi arrangements.(3) We gave answers to Holm's questions for high order freeness of hyperplane arrangements.
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| Academic Significance and Societal Importance of the Research Achievements |
拡張Hamming重み多項式は符号の誤り訂正能力にかかわる最小重みの情報を含む重要な多項式であり、誤り訂正符号の分野において興味の対象となっている。一方で、拡張Hamming重み多項式の計算は困難で、具体的な表示が与えられている符号のクラスは多くない。本研究では、拡張Hamming重み多項式と本質的に同じ多項式であるCoboundary多項式を、Catalan配置に関する超平面配置の理論を使いながら計算した。このようにそれぞれの分野をつなぐ具体例となった。
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Report
(4 results)
Research Products
(11 results)
