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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:277  下載:3 
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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. Introduction to codes 7 2. Reed-Muller codes 9 2.1. De nition 9 2.2. Properties of Reed-Muller codes 10 3. Decoding Reed-Muller codes 14 4. Permutation decoding 17 5. Decoding rst order Reed-Muller code by permutation decoding method 20 6. Using permutation to increasing the speed of decoding rst order Reed-Muller codes 23 7. Conclusion 28 Appendix A. Table 29 Appendix B. Code 36 References 41

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