Matroids, Quantum Information Theory, and Codes

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400187
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kumamoto University
• Principal Investigator: Keisuke Shiromoto 熊本大学, 大学院先端科学研究部(工), 教授 (00343666)
• 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)
• 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)
• Research Collaborator: Thomas Britz University of New South Wales, School of Mathematics, Senior Lecturer
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: マトロイド / 量子情報 / 線形符号

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.

Free Research Field

代数的符号理論