Research on families of maximal triply even codes and related mathematical structures
| Project/Area Number |
17K05153
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Hirosaki University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2017-04-01 – 2020-03-31
|
| Project Status |
Completed (Fiscal Year 2019)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | 代数的組合せ論 / 符号理論 / 離散幾何 / 組合せデザイン / 散在型有限単純群 / グラフ理論 / 極大立方重偶符号 / 自己双対符号 / 散在型単純群 / 群論 / 代数的符号理論 |
|---|
| Outline of Final Research Achievements |
We obtained the following results.
(1) From some strongly regular graphs, we constructed triply even codes. We showed the maximality, the weight distribution, the automorphism groups and showed some other equipped structures. (2) On a series of triply even codes constructed from finite geometries, we showed some lemmas. (3) From triply even codes, we constructed some secret sharing schemes. (4) We made some sense of a lattice over a quadratic field constructed from a quaternary code in relations to triply even codes. (5) We calculated some subgroups of the Conway0 group which is the automorphism group of the Leech lattice.
|
| Academic Significance and Societal Importance of the Research Achievements |
これまでの研究を通して、立方重偶符号が共形場理論、有限群論、保型形式論、情報理論などの様々な数理構造と関連することが明らかとなっている。
立方重偶符号の研究を通して、頂点作用素代数の性質が明らかになることや、散在型単純群やLie型の有限単純群の系列に関する新たな視点が得られることは意義深い。
|
Report
(4 results)
Research Products
(14 results)
