Research on combinatorics over Galois rings
Project/Area Number |
20540014
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Kanazawa University |
Principal Investigator |
YAMADA Mieko 金沢大学, 数物科学系, 教授 (70130226)
|
Co-Investigator(Kenkyū-buntansha) |
菅野 孝史 金沢大学, 数物科学系, 教授 (30183841)
|
Project Period (FY) |
2008 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
Keywords | ガロア環 / 差集合 / 符号理論 / ガウス和 / designs / Hadamard行列 / ガロア和 |
Research Abstract |
We constructed infinite families of difference sets over Galois rings of characteristic an even power of 2. The difference set over a Galois ring of characteristic 2^n is embedded in the ideal part of the difference set over a Galois ring of characteristic 2^n+2 . We introduced a new operation in a Galois ring and the Gauss sums associated with the character under this new operation play an important role of the proof. Furthermore, we proved there exist Reed-Muller codes with embedding system and showed several properties of them.
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Report
(6 results)
Research Products
(41 results)