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研究生: 歐陽中彥
Ouyang, Jung-Yan
論文名稱: 論二元極自對偶碼的分類
On the Classification of Binary Extremal Self-dual Codes
指導教授: 俞勇
Yu, Yung
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: 2004
畢業學年度: 92
語文別: 英文
論文頁數: 89
中文關鍵詞: 二元極自對偶碼
外文關鍵詞: weight enumerators, binary extremal self-dual codes
相關次數: 點閱:93下載:2
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    The object of this study is mainly discuss the binary extremal self-dual codes. For Type I codes, we are going to investigate the weight enumerators and relative data from length 2 to length 100. For Type II codes, we investigate those from length 8 to length 96.

    Chapter 1 INTRODUCTION …..…………...…….……………………. 1 1.1 Basic Definitions and Preliminaries ………………………... 1 1.2 Two Fundamental Theorems ……………………………….. 4 Chapter 2 BINARY EXTREMAL SELF-DUAL CODES ……...……… 7 2.1 Building-up method ………………………………….……... 8 2.2 Type I Codes of Length Up To 100 …………………..…….. 13 2.2.1 Length 2 …………..……..………………………………. 13 2.2.2 Length 4 ………………....………………………………. 13 2.2.3 Length 6 …………………………………………………. 13 2.2.4 Length 8 …………………………………………………. 14 2.2.5 Length 10 ………..………………………………………. 14 2.2.6 Length 12 …..……………………………………………. 15 2.2.7 Length 14 ..………………………………………………. 15 2.2.8 Length 16 …..……………………………………………. 16 2.2.9 Length 18 …..……………………………………………. 17 2.2.10 Length 20 ……..…………………………………………. 17 2.2.11 Length 22 …..……………………………………………. 20 2.2.12 Length 24 ……………..…………………………………. 20 2.2.13 Length 26 ……………..…………………………………. 21 2.2.14 Length 28 ……..…………………………………………. 22 2.2.15 Length 30 …..……………………………………………. 23 2.2.16 Length 32 …..……………………………………………. 28 2.2.17 Length 34 …..……………………………………………. 28 2.2.18 Length 36 ……..…………………………………………. 29 2.2.19 Length 38 …..……………………………………………. 30 2.2.20 Length 40 ……..…………………………………………. 31 2.2.21 Length 42 …..……………………………………………. 33 2.2.22 Length 44 …..……………………………………………. 35 2.2.23 Length 46 …..……………………………………………. 40 2.2.24 Length 48 ……..…………………………………………. 40 2.2.25 Length 50 …..……………………………………………. 41 2.2.26 Length 52 …..……………………………………………. 41 2.2.27 Length 54 …..……………………………………………. 42 2.2.28 Length 56 …..……………………………………………. 47 2.2.29 Length 58 ……..…………………………………………. 48 2.2.30 Length 60 …..……………………………………………. 52 2.2.31 Length 62 ……..…………………………………………. 54 2.2.32 Length 64 …..……………………………………………. 55 2.2.33 Length 66 …..……………………………………………. 58 2.2.34 Length 68 …..……………………………………………. 59 2.2.35 Length 70 ……..…………………………………………. 60 2.2.36 Length 72 …..……………………………………………. 61 2.2.37 Length 74 …..……………………………………………. 61 2.2.38 Length 76 …..……………………………………………. 62 2.2.39 Length 78 …..……………………………………………. 63 2.2.40 Length 80 ……..…………………………………………. 64 2.2.41 Length 82 …..……………………………………………. 65 2.2.42 Length 84 …..……………………………………………. 65 2.2.43 Length 86 …..……………………………………………. 66 2.2.44 Length 88 …..……………………………………………. 67 2.2.45 Length 90 …..……………………………………………. 67 2.2.46 Length 92 ……..…………………………………………. 68 2.2.47 Length 94 …..……………………………………………. 69 2.2.48 Length 96 …..……………………………………………. 69 2.2.49 Length 98 …..……………………………………………. 70 2.2.50 Length 100 ………………………………………………. 70 2.3 Type II Codes of Length Up To 96 …………………..……... 72 2.3.1 Length 8 …………………………………………………. 72 2.3.2 Length 16 …..……………………………………………. 72 2.3.3 Length 24 …..……………………………………………. 73 2.3.4 Length 32 …..……………………………………………. 73 2.3.5 Length 40 ………..………………………………………. 74 2.3.6 Length 48 …..……………………………………………. 77 2.3.7 Length 56 …..……………………………………………. 77 2.3.8 Length 64 ……..…………………………………………. 79 2.3.9 Length 72 ……..…………………………………………. 81 2.3.10 Length 80 …..……………………………………………. 82 2.3.11 Length 88 …..……………………………………………. 82 2.3.12 Length 96 ……………..…………………………………. 83 REFERENCES ………...………………………………………....…... 85

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