2012 Fiscal Year Final Research Report
Challenging to construction of an extremal doubly even self-dual code of length 72
| Project/Area Number |
23654029
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Yamagata University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
KITAZUME Masaaki 千葉大学, 大学院・理学研究科, 教授 (60204898)
SHIMAKURA Hiroki 東北大学, 大学院・情報科学研究科, 准教授 (90399791)
|
|---|
| Project Period (FY) |
2011 – 2012
|
| Keywords | 自己双対符号 / 格子 / 組合せデザイン |
|---|
| Research Abstract |
In this research proect, I tried to construction of an extremal doubly even self-dual code of length 72. The existence of such a code is a famous problem in algebraic coding theory. In this process, a 72-dimensional optimal odd unimodular lattice was constructed for the first time. Also, it was shown that there is an extremal Type II _<2k>-code of length 72 for an integer satisfying that is even and is greater than or equal to 4.
|
