摘要(ABSTRACT)摘要(ABSTRACT)
在1990年,Conway與Sloane的論文中,有可能為極端自對偶[62,31,12]碼之權計算式。
其中β是未定的參數。
1999年,Harada建構出一個對應於β=10之極端自對偶[62,31,12]碼。現在我們也建構出一個對應於β=10之極端自對偶[62,31,12]碼,不等價於Harada所建構的。

章節 標 題 頁數
誌謝 (Acknowledgment)…………………………………….i
摘要(Abstract)………………………………………………ii
目錄 (Table of Content)………………………………iii
第一章 緒論 (Introduction)………………………………………. 1
第二章 長度60之極端自對偶碼…………………………….……… 3
(EXTREMAL SELF-DUAL CODES OF LENGTH 60)
第三章 長度62之極端自對偶碼………………………………….. 17
(EXTREMAL SELF-DUAL CODES OF LENGTH 62)
3-1 Kim的定理………………………………………………. 17
3-2 極端自對偶[62,31,12]碼,C62…………………………. 17
3-3 極端自對偶[62,31,12]碼,T62………………..………. 17
3-4 定理3.1: C62與T62不等價……………….…..…….. 18
第四章 附註(Reference)………….…………………………………. 23

參考：
[1] J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, vol. 36, no. 6, pp. 1319-1333, Nov, 1990.
[2] H. P. Tsai, Existence of certain extremal self-dual codes, PH. D. thesis, University of Illinois at Chicago, 1992.
[3] T.A. Gulliver and M. Harada, Weight enumerators of extremal singly-even[60,30,12] codes ,IEEE Trans. Inform. Theory, vol. 42, no. 2, pp. 658-659 March 1996.
[4] H.P. Tsai and Y.J. Jiang , Some new extremal self-dual [58,29,10] codes, IEEE Trans. Inform. Theory, vol. 44, pp. 812-814, Mar, 1998.
[5] M. Harada, Construction of an extremal self-dual code of length 62, IEEE Trans. Inform. Theory, vol. 45, pp. 1232-1233, May, 1999.
[6] 蔡漢彬，自對偶[60,30,12]碼之不等價碼，NSC89-2115-M-031-004.
[7] J. L. Kim, New extremal self-dual codes of lengths 36, 38, and 58, IEEE Trans. Inform. Theory, vol. 47, no. 1, pp. 386-393, January, 2001.