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| 研究生： |
曾筠茜 Tseng, Yun-Chien |
|---|---|
| 論文名稱： |
On Cyclic Codes Over Finite Chain Rings and Self-Dual Cyclic Codes Over Finite Fields On Cyclic Codes Over Finite Chain Rings and Self-Dual Cyclic Codes Over Finite Fields |
| 指導教授： |
紀文鎮
Chi, Wen-Chen |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2015 |
| 畢業學年度： | 103 |
| 語文別： | 英文 |
| 論文頁數： | 21 |
| 中文關鍵詞： | Finite chain rings 、Cyclic codes 、Self-dual cyclic codes |
| 英文關鍵詞： | Finite chain rings, Cyclic codes, Self-dual cyclic codes |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：76 下載：20 |
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Theorems in coding theory has extended from fields Fq to finite chain rings R. In this thesis, we introduce the structure of R and properties over R, discuss theorems for codes C over R, talk about self-dual cyclic codes over finite fields Fq, and give examples for codes over R and Fq.
Theorems in coding theory has extended from fields Fq to finite chain rings R. In this thesis, we introduce the structure of R and properties over R, discuss theorems for codes C over R, talk about self-dual cyclic codes over finite fields Fq, and give examples for codes over R and Fq.
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[2] Yan Jia, San Ling, Chaoping Xing, On Self-Dual Cyclic Codes Over Finite Field, IEEE Trans. Inf. Theory, Vol:57, No:4, pp. 2243-2251, (Apr. 2011)
[3] Bocong Chen, San Ling, Guanghui Zhang, Self-Dual Cyclic Codes Over Finite Chain Ring, (2014)
[4] Vera Pless, Patrick Sole, Zhongqiang Qian, Cyclic Self-Dual Z4-Codes, Finite Fields Appl., Vol:3, pp. 48-69 (1997)
[5] Bernard R. McDonald, Finite Rings with Identity, in Pure and Applied Math- ematics. New York: Marcel Dekker vol 28, (1974)
[6] M. F. Atiyah, I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Series in Mathematics, (1994)
