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研究生:林俊志
研究生(外文):Chung-Chih Lin
論文名稱:二次剩餘碼(89,45,17)之研究
論文名稱(外文):A study On the Quadratic Residue code (89,45,17)
指導教授:李珠矽
指導教授(外文):Ju-Shih Lee
學位類別:碩士
校院名稱:國立高雄師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:英文
論文頁數:40
中文關鍵詞:二次剩餘碼(894517)編碼
外文關鍵詞:Quadratic Residue code(894517)code
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代數應用在編碼的領域上已經應用的很廣泛了,尤其是在編二次剩餘碼以及解二次剩餘碼更是已經在很多篇的論文應用及討論過了。在這一篇論文中,我們仍是運用代數的方法去解長度為8m+1的二次剩餘碼。而在論文中我所討論的是專對於(89,45,17)這一個二次剩餘碼的解錯討論。

Algebraic approaches to the decoding of the quadratic residue QR-codes were studied in many articles. In [4], a decoding algorithm was given for the (41,21,9) binary QR-code. In this thesis, some new more general properties are found for the syndromes of the subclass of binary QR codes of length n=8m+1. Using these properties the new theorems needed to decode this subclass of the QR codes are obtained and proved. As an example of the application of these theorems, a new algebraic decoding algorithm for the (89,45,17) binary QR-code is presented.

1.Introduction.......................................1
2.Linear Code........................................4
3.Cyclic Code........................................8
4.Quadratic Residue Code............................13
5.Decoding (89,45,17)...............................19
6.Conclution and Further Research...................40

[1]Ad\'{a}mek, J.: " Foundations of Coding", John-Wiley and Sons, 1991.
[2]Berlekamp, E.: "Algebraic Coding Theory", Agean Park Press, 1984.
[3]Chang, Y., Truong, T.K. and Reed, I.S.: "Fast algorithm in determining free polynomials over GF(2)". (submitted to "Finite Fields and their Applications")
[4]Chen, X.: "Binary Quadratic Residue Codes For Random Error Correction", University of Southern California Ph.D. Thesis, November 1993.
[5]Herstein, I.N.: "Topics in Algebra", Second Edition, John-Wiley and Sons, New York, 1975.
[6]Lidl, R., and Pilz, G.: "Applied Abstract Algebra", Springer, New York, 1997.
[7]Pless, V.: "Introduction to the Theory of Error-Correcting Codes", Second Edition, John-Wiley and Sons, 1989.
[8]Reed, I.S., Truong, T.K., and Yin, X.: "Algebraic Decoding of the (41,21,9) Quadratic Residue code", IEEE Trans., 1992, IT -38, (3), pp. 974-986.
[9]Reed, I.S., Yin, X., and Truong, T.K.: "Decoding the (24,12,8) Golary Code", Proc. IEEE, 1990,137, (3), pp. 202-206.
[10]Reed, I.S., Yin, X., and Truong, T.K.: "Algebraic Decoding of the (32,16,8) Quadratic Residue Code", IEEE Trans., 1990, IT -36, (4), pp. 876-880.
[11]Roman, S.: "Coding and Information Theory", Springer, New York, 1991.
[12]Yin, X.: "Decoding The Binary Quadratic Residue Codes", University of Southern California Ph.D. Thesis, May 1993.
[13]王新梅,肖國鎮:《糾錯碼》,儒林圖書公司,1993
[14]肖國鎮,卿斯漢:《編碼理論》,大陸國防工業出版社,1993
[15]侯源安:《代數學》,東華書局,1996

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