2020 Fiscal Year Final Research Report

Coding Theoretical Approach to the Representation and Covering Problems for Matroids(Fostering Joint International Research)

Research Project

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Project/Area Number	16KK0103
Research Category	Fund for the Promotion of Joint International Research (Fostering Joint International Research)
Allocation Type	Multi-year Fund
Research Field	Foundations of mathematics/Applied mathematics
Research Institution	Kumamoto University
Principal Investigator	Shiromoto Keisuke 熊本大学, 大学院先端科学研究部(工), 教授 (00343666)
Project Period (FY)	2017 – 2020
Keywords	符号理論 / マトロイド / 組合せ論 / 非線形符号 / 最小被覆数
Outline of Final Research Achievements	In this fostering joint international research project, we focused on some matroid problems in our based research project on algebraic coding theory and then we mainly had the following results: (1) We gave some constructions of non-linear codes from powerful sets. (2) We derived an upper bound on covering numbers of matroids and we gave some constructions of matroids which attain the bound.
Free Research Field	代数的符号理論
Academic Significance and Societal Importance of the Research Achievements	符号理論とは，デジタル情報を伝送または記録する際に生じる誤りを理論的に訂正するための誤り訂正符号の理論であり，その代数構造に着目して数理的研究をおこなうことが代数的符号理論である．本国際共同研究において得られた研究成果については，主に誤り訂正能力の高い非線形符号の構成法や秘密分散共有法や暗号理論等の情報セキュリティ分野において情報の秘匿化に有用なマトロイドの構成法を提案することで，今後の高度情報化社会におけるIoTやデータサイエンス分野への貢献が期待される．