| 研究生: |
李至晟 Li, Jhih-Cheng |
|---|---|
| 論文名稱: |
循環橫向碼 Loop Transversal Code |
| 指導教授: |
柯文峰
Ke, Wen-Fong |
| 學位類別: |
碩士 Master |
| 系所名稱: |
理學院 - 數學系應用數學碩博士班 Department of Mathematics |
| 論文出版年: | 2025 |
| 畢業學年度: | 113 |
| 語文別: | 英文 |
| 論文頁數: | 25 |
| 中文關鍵詞: | 錯誤更正碼 、線性碼 、循環 、橫向 |
| 外文關鍵詞: | Error correcting code, Linear code, Loop, Transversal |
| 相關次數: | 點閱:99 下載:6 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
在本文中,我們將回顧名為循環橫向碼的線性錯誤更正碼。相較於直接建構錯誤更正碼,再行分析,循環橫向碼則由一個我們希望更正的錯誤集合來構建。
In this thesis, we will review the construction of loop transversal codes, which are a kind of linear error-correcting codes. Contrary to building the code directly, loop transversal codes are constructed by a set of errors that we want to correct.
[1] Elwyn R Berlekamp, Algebraic Coding Theory (Revised Edition), 2015, World Scientific. 1.1, 2.2
[2] Vera Pless, Introduction to the Theory of Error-Correcting Codes (Third Edition), 1998, Wiley-Interscience.
[3] W.Cary Huffman, Jon-Lark Kim and Patrick Sole, Concise Encyclopedia of Coding Theory, 2021, CRC Press. 1.2, 1.3, 1.4, 2.1, 2.2, 2.3
[4] Hala O Pflugfelder, Quasigroups and loops: Introduction (Sigma series in puremathematics), 1990, Heldermann. 2.8 19
[5] Charles J. Colbourn and Jeffrey H. Dinitz, Handbook of Combinatorial Designs(2nd Edition), 2007, Chapman & Hall. 2.8
[6] Eugene Kuznetsov, Transversals in loops. 3. Loop transversals, Buletinul Academiei de S ¸tiint ¸e a Republicii Moldova.Matematica, Number 3(67), 2011.2.6, 2.8, 2.10, 2.11
[7] Jonathan D.H. Smith, An Introduction to Quasigroups and Their Representations, 2007, Chapman & Hall. 2.2, 2.14, 3.1, 3.3, 3.2, 3.5
[8] Jonathan D.H. Smith, Loop transversals to linear codes, J. Combin. System.Sci. 17(1992) 2-8 1
[9] F. A. Hummer, Loop Transveral Codes, ProQuest LLC, Ann Arbor, MI, 1992.1, 3.2, 3.9
[10] F. A. Hummer and Jonathan D.H. Smith, Greedy Loop Transversal Codes, Metrics, and Lexicodes, Journal of Combinatorial Mathematics and Combinatorial Computing, 22(1996) 143-155. 3.2
[11] R. Aydinyan, Loop Transversal Codes over Finite Rings, ProQuest LLC, Ann Arbor, MI, 2005. 1, 3.2, 4, 4.1, 4.3, 4.4