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| 研究生： |
楊茂昌 Yang, Mao Chang |
|---|---|
| 論文名稱： |
Wilbrink定理的探討 Variations on Wilbrink's Theorem |
| 指導教授： |
陳永秋
Tan, Eng Tjieo |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 1994 |
| 畢業學年度： | 82 |
| 語文別： | 英文 |
| 論文頁數： | 43 |
| 中文關鍵詞： | 可換差集 、乘數 、離散型富利葉轉換 、p-進位特徵函數 、乘數猜測 、Hall 猜測 |
| 外文關鍵詞： | Abelian difference sets, multipliers, Discrete Fourier Transform (DFT), p-adic characters, multiplier's conjecture, Hall's conjecture |
| 相關次數： | 點閱：92 下載：0 |
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本文希望藉著K.T Arasu, D.Jungnickel, A.Pott推廣Wilbrink定理的方法去尋找Wilbrink等式的推廣式在p<sup>k</sup>∥n,k≧4的推廣式和其應用。
In this thesis we formulate and provide rigorous proofs of Wilbrink's theorem and it's variations due to Arasu, A.Pott and D.Jungnickel. some questions on further generalizations of Wilbrink's theorem are discussed; known generalization are study in A.Pott's dissertation.
謝詞
Abstract
中文簡介-----1
Contents-----2
1 Introduction-----3
2 Preliminaries on algebraic design theory-----6
2.1 The theory of discrete Fourier transformation (DFT)-----7
2.2 Codes defined by symmetric design-----11
2.3 Multiplier of difference sets-----15
3 Proofs of Wilbrink's theorem-----17
3.1 Wilbrink's original proof-----18
3.2 Arasu's proof for Theorem 2-----19
3.3 Jungnickel's proof for Theorem 3-----20
3.4 Pott's proof for Theorem 3-----22
4 Conjectures related to Wilbrink's theorem-----26
5 Pott's generalizations of Wilbrink's theorem-----29
5.1 Pott's p-adic approach to theory of DS-----30
5.2 Pott's proof for generalizations of Wilbrink's Theorem-----32
6 Discussion-----37
(限達賢圖書館四樓資訊教室A單機使用)