Combinatorial codes and their decoding algorithms related to various information transmission systems

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340016
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nagoya University
• Principal Investigator: JIMBO Masakazu 名古屋大学, 情報科学研究科, 教授 (50103049)
• Co-Investigator(Kenkyū-buntansha): KURIKI Shinji 大阪府立大学, 工学研究科, 教授 (00167389) ; MISHIMA Miwako 岐阜大学, 工学部, 准教授 (00283284) ; KANAMORI Takafumi 名古屋大学, 情報科学研究科, 准教授 (60334546) ; SHIROMOTO Keisuke 熊本大学, 自然科学研究科, 教授 (00343666) ; SAWA Masanori 神戸大学, 大学院システム情報学研究科, 准教授 (50508182)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 組合せデザイン / 衝突回避符号 / 量子ジャンプ符号 / 光直交符号 / t-MOD / 球面デザイン / グループテスト

Outline of Final Research Achievements

In this project, the following results for combinatorial structures related to information communication systems are obtained. (i) Constructions of conflict-avoiding codes with weights three and four are obtained. (ii) Constructions of affine-invariant SQSs are obtained. (iii) Quantum jump codes are charactelized as families of mutually orthogonal t-designs and their existence are discussed. (iv) Constructions of some optimal Euclidean designs on concentric spheres are obtained. (v) Optimality, in the sense of detecting probability of positive items, of a regular bipartite graph representing a group testing is clarified.

Free Research Field

離散数学とその応用