| 研究生: |
蘇博俞 Su, Po-Yu |
|---|---|
| 論文名稱: |
一階Reed-Muller碼的轉置解碼 Permutation decoding of first order Reed-Muller 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: | 2014 |
| 畢業學年度: | 102 |
| 語文別: | 英文 |
| 論文頁數: | 41 |
| 中文關鍵詞: | Reed-Muller編碼 、轉置解碼 |
| 外文關鍵詞: | Reed-Muller code, permutation decoding |
| 相關次數: | 點閱:118 下載:3 |
| 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 |
在文章一開始會先介紹Reed-Muller 編碼的性質,接著介紹如何用
多數邏輯來解碼Reed-Muller。接著我們去介紹轉置解碼與一些在一階
Reed-Muller 編碼上用轉置解碼的結果。最後我們會使用GAP 去演繹
和猜想一些在錯誤與資訊字元之間的關係。
We study Reed-Muller code. First we list some good prorerties of
Reed-Muller code, and show how to decode Reed-Muller code by majority
logic. Then we look at permutation decoding, and record some
results for decoding first order Reed-Muller code using permutation decoding
method. Finally, we use GAP to perform the decoding and
present some relation between the errors and the information words.
[1] E.F.Assmus & J.D.Key, Designs And Their Codes, Cambridge University Press, Great Britain at
the University Press, 1992.
[2] B. Cooke, Reed Muller Error Correcting Codes, MIT Undergraduate J. Math., vol. 1, p.21{p.26,
1999.
[3] D.G.Ho man, D.A.Leonard, C.C.Lindner, K.T.Phelps, C.A.Rodger, J.R.Wall, Coding Theory:
the essentials, Marcel Dekker, the Unites States of America, 1992.
[4] J.D.Key, T.P. McDonough, V.C. Mavron, Information sets and partial permutation decoding for
codes from nite geometries, Finite Fields Appl. 12(2006) 232-247.
[5] J.D.Key, T.P. McDonough, V.C. Mavron, Reed-Muller codes and permutation decoding, Discrete
Mathematics 310(2010) 3114-3119.
[6] J.H.van Lint, Intrduction to Coding Theory, Springer-Verlag New York Heidelberg Berlin, the
Unites States of America, 1982.
[7] F.J. MacWilliams, Permutation decoding of systematic codes, Bell Syst. Tech. J. 43(1964) 485-505
[8] Vera Pless, Introduction to the Theorey of Error-Correcting Codes, Wiley-Interscience Publication,
Canada, 1998.
[9] Steven Roman, Coding and Information Theory, Springer-Verlag New York, the Unites States of
America, 1992.
[10] P.Seneviratne, Partial permutation decoding for the rst-order Reed-Muller codes, Discrete Math-
ematics 309(2009) 1967-1970.