簡易檢索 / 詳目顯示

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 Introduction 2 2 Preliminaries 3 2.1 HammingCode 3 2.2 Looptransversal 5 3 Looptransversalcode 9 3.1 Observation 9 3.2 Generalconstruction 13 3.3 Greedyconstruction 14 4 Greedylooptransversalcode 17 Reference 19

    [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

    下載圖示 校內:立即公開
    校外:立即公開
    QR CODE