Challenging of the existence problem of a certain self-dual code through combinatorial designs and lattices

2015 Fiscal Year Final Research Report

• Project/Area Number: 26610032
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tohoku University
• Principal Investigator: Harada Masaaki 東北大学, 情報科学研究科, 教授 (90292408)
• Co-Investigator(Renkei-kenkyūsha): MUNEMASA Akihiro 東北大学, 大学院情報科学研究科, 教授 (50219862) ; SHIMAKURA Hiroki 東北大学, 大学院情報科学研究科, 准教授 (90399791)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: 組合せ論 / 代数的符号理論 / 自己双対符号 / 格子 / 組合せデザイン

Outline of Final Research Achievements

In this project, I studied self-orthogonal designs including a self-orthogonal 5-(72,16,78) design, where the existences of such a design and an extremal doubly even self-dual code of length 72 are equivalent, with Akihiro Munemasa.
Using the classification of unimodular lattices, I gave some classification of self-dual Zk-codes. In addition, I studied supplementary difference sets related to complex spherical 2-codes.

Free Research Field

代数的符号理論