A study of combinatorics over Galois rings
| Project/Area Number |
24540013
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tokyo Woman's Christian University (2014)
Kanazawa University (2012-2013) |
|---|
Principal Investigator |
YAMADA Mieko 東京女子大学, 現代教養学部, 研究員 (70130226)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MOMIHARA Koji 熊本大学, 教育学部, 講師 (70613305)
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | ガロア環 / 差集合 / ガウス和 / Hadamard行列 / difference family / 符号 / 符号理論 / アダマール行列 |
|---|
| Outline of Final Research Achievements |
We gave a new approach and a new perspective on the study of combinatorics, that is,recognizing a combinatorial structure over finite fields and Galois rings as an image of a subset of a local field by natural projections. We obtained an infinite family of Menon-Hadamard difference sets over Galois rings of characteristic a power of 2 from a subset of 2-adic field by natural projections, which has a nested structure. Furthermore we showed that there exist difference families and Hadamard matrices over Galois rings of characteristic 4. For odd characteristics, we constructed a decoding algorithm of BCH codes with at most 2 errors. For a characteristic a square of a prime and an extension degree 2, we constructed difference families and Hadamard matrices.
In addition to the above results, we constructed Cayley graphs and their lifting and provided a new insight of the classification of skew Hadamard matrices over finite fields.
|
Report
(4 results)
Research Products
(40 results)
