| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We would like to obtain progress of optimal spherical codes in this research project. One of major problems of optimal spherical codes is to find a spherical finite set which has maximum minimum-distance between distinct points among the equal-sized spherical sets. The linear programming bound (Delsarte's method) is a powerful tool to obtain a bound for the size of spherical sets for given distances. For regular graphs, we gave the ``dual'' version of the linear programming bound. The spectrum (the eigenvalues of the adjacency matrix) of a regular graph has some dual relationship to the distances on a finite spherical set. We can expect similar results between spherical codes (spherical finite sets) and regular graphs, and developments of both objects from each other.
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