2015 Fiscal Year Final Research Report
Constructions of combinatorial designs leading to quantum codes and protocol sequences for multiple-access communication channel
| Project/Area Number |
25400200
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Gifu University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
JIMBO MASAKAZU 中部大学, 現代教育学部, 教授 (50103049)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 衝突回避符号 / デザインの分割 / アフィン幾何 |
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| Outline of Final Research Achievements |
t-SEED, a class of combinatorial designs which gives quantum jump codes, has been characterized and some recursive constructions of t-SEEDs have been obtained. It is known that the 2-design formed by the planes in affine geometry can be decomposed into subdesigns, which satisfies a property of t-SEEDs. We have shown a decomposition of the 2-design formed by the planes in AG(2n,4) into subdesigns stabilized by the action of the affine general linear group AGL(1,pow(4,2n)), which gives the larger number of subdesigns than the previously known decomposition.
As for confilict-avoiding codes (CAC), some explicit series of tight/optimal equi-difference CACs and tight CACs of odd length and weight 3 have been provided. Furthermore, restricting to equi-difference codes, several series of infinite number of optimal equi-difference CACs have been obtained together with the recursion formulae of the number of codewords.
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| Free Research Field |
組合せ論
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