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| 研究生： |
洪崇峰 Hung, Chung-Feng |
|---|---|
| 論文名稱： |
Structures of Constacyclic Codes of Length 2p^s over Finite Fields Structures of Constacyclic Codes of Length 2p^s 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： | 28 |
| 中文關鍵詞： | finite fields 、constacyclic codes 、dual codes 、polynomial generators |
| 英文關鍵詞： | finite fields, constacyclic codes, dual codes, polynomial generators |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：134 下載：31 |
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無中文摘要
We first recall the algebraic structures of constacyclic
codes. Then, we describe constacyclic codes by finding their generator polynomials, and we also give a way to find the dual codes of constacyclic codes as well as to discuss the conditions of existence of self-dual codes of cyclic and negacyclic codes of length 2p^s over F_p^m. Finally, we give structures of all constacyclic codes of length 2p^s over F_p^m via isomorphisms between cyclic codes, negacyclic codes and constacyclic codes.
References
[1] Hai Q. Dinh, Repeated-root constacyclic codes of length 2p^s, Finite Fields and Their Applications 18(1) (2012), 133-143.
[2] Hai Q. Dinh, Repeated-Root Cyclic and Negacyclic Codes of Length 6p^s, Contemporary Math. 609 (2014), 69-88.
[3] Bocong Chen, Yun Fan, Liren Lin, and Hongwei Liu, Constacyclic Codes over Finite Fields, Finite Fields and Their Applications 18(6) (2012), 1217-1231
[4] W. Cary Hu man and Vera Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, Cambridge, 2003.
[5] San Ling and Chaoping Xing, Coding Theory: A First Course, Cambridge University Press, Cambridge, 2004.
[6] Thomas W. Hungerford, Algebra, Springer-Verlag, New York, 1974.
