Graph representations of combinatorial structures

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04976
• 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: Shizuoka University
• Principal Investigator: Araya Makoto 静岡大学, 情報学部, 教授 (70303526)
• Co-Investigator(Kenkyū-buntansha): 原田 昌晃 東北大学, 情報科学研究科, 教授 (90292408)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: グラフ表現 / 誤り訂正符号 / 組合せデザイン / 有限環

Outline of Final Research Achievements

By a graph representation of a linear code over finite ring, we give classifications of a certain class of self-complementary codes for modest lengths. As a consequence we give quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices. We classify ternary maximal self-orthogonal codes of lengths 21,22 and 23 by a graph representation.
We classify partially balanced incomplete block designs by given association schemes and its automorphism groups. For bipartite graphs and association schemes, we classify some partially balanced incomplete block designs. Each graphs are a representation of designs.

Free Research Field

代数的組合せ論