最佳球面編碼與設計;Optimal Spherical Codes and Designs

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/84767

Title:	最佳球面編碼與設計;Optimal Spherical Codes and Designs
Authors:	俞韋亘
Contributors:	數學系
Keywords:	離散幾何;等角直線叢;球面設計;最大二距離;三距離集合;discrete geometry;equiangular lines;spherical designs;maximum spherical two-distance set;spherical three-distance set
Date:	2020-12-08
Issue Date:	2020-12-09 10:54:34 (UTC+8)
Publisher:	科技部
Abstract:	我們將研究離散幾何的經典問題: 最佳球面編碼與設計問題。在n 維空間中球面最大的s 距離集合問題，從上個世紀 70年代開始就陸續有數學家關心與獲取一系列的進展。然而對大部分的維度n 還有距離的個數s，仍然是未知的問題。我們將努力用手上的工具與學習新的知識方法來對這一列別的問題獲取新的研究成果。 ;The goals of this research project are to study and work on classical problems indiscrete geometry area, called optimal spherical codes and designs. The notion ofoptimal spherical codes and designs is indeed broad. Such as the kissing numberproblem and sphere packing problem also can be regarded as the types of optimalspherical codes problems. Delsarte, Goethals and Seidel defined the notion ofspherical s-distance sets in 1977 and derived their upper bounds. However, for most of the cases of what is the maximum size of spherical s-distance sets are still open. The maximum equiangular lines problems in is also one type of that problem. Although we obtain series of new result for the maximum size of equiangular line problems but there are still quite many interesting open casesto work on.
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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