臺灣博碩士論文加值系統

1990年在Conway and Sloane[5]的論文中，對於單偶極端自對偶[54, 27, 10]碼，其可能之權計算式(weight enumerator)分別為：
W54,1 = 1+(351−8β)y10+(5,031+24β)y12+(48,492+32β)y14+……, where 0≦β≦43.
W54,2 = 1+(351−8β)y10+(5,543+24β)y12+(43,884+32β)y14+……, where 12≦β≦43. 其中β為一個未定的參數。
現在我們建構了一個對應於W54,1，β =16與一個對應於W54,2，β =21的不等價之極端自對偶[54, 27, 10]碼。

1990年在Conway and Sloane[5]的論文中，對於單偶極端自對偶[64, 32, 12]碼，其可能之權計算式分別為：
W64,1 = 1+(1,312+16β)y12+(22,016−64β)y14+(239,148−32β)y16+……, where 14≦β≦284.
W64,2 = 1+(1,312+16β)y12+(23,040−64β)y14+(228,908−32β)y16+……, where 0≦β≦277. 其中β為一個未定的參數。
現在我們建構了一個對應於W64,2，β =15的新極端自對偶[64, 32, 12]碼。

1997年在Dougherty, Gulliver, and Harada[6]的論文中，對於單偶極端自對偶[66, 33, 12]碼，其可能之權計算式分別為：
W66,1 = 1+1,690y12+7,990y14+302,705y16+ 867,035y18+ …… ,
W66,2 = 1+(858+8β)y12+(18,678−24β)y14+(201,201−48β)y16+…… , where 0≦β≦778.
W66,3 = 1+(858+8β)y12+(18,166−24β)y14+(205,809−48β)y16+…… , where 14≦β≦756. 其中β為一個未定的參數。
現在我們建構了九個對應於W66,2，β =12, 21, 25, 28, 30, 34, 39, 58, 184與廿二個對應於W66,3，β = 25, 29, 49, 50, 51, 53, 54, 56, 57, 59, 61, 68, 70, 72, 74, 76, 78, 80, 82, 98, 106, 112的新極端自對偶[66, 33, 12]碼。

1998年在Buyuklieva and Boukliev[2]的論文中，對於單偶極端自對偶[68, 34, 12]碼，其可能之權計算式分別為：
W68,1 = 1+(442+4β)y12+(10,864−8β)y14+(223,623−36β)y16+…… , where 104≦β≦1358.
W68,2 = 1+(442+4β)y12+(14,960−8β−256γ)y14+……, where 0≦γ≦11 and 14γ≦β≦1870−32γ. 其中β、γ為一個未定的參數。
現在我們建構了兩個對應於W68,1，β =117, 120與四百九十九個對應於W68,2，
γ=0，β =33, 37,…, 44, 46, 66, 116,…, 135, 137,…, 169, 171,…, 203, 205,…, 237, 239,…, 262, 264,…, 270, 273, 274, 276, 278, 282, 288, 290；
γ=1，β =49, 52,…, 60, 62, 66,…, 69, 116,…, 211, 213, 216；
γ=2，β =61, 69, 116,…, 215, 219, 220, 222, 224, 225, 230；
γ=3，β =85, 91,…, 122, 124, 126,…, 137, 139,…, 175, 177, 178, 180, 182, 184, 186, 188, 189, 191, 192, 194, 196, 203, 207, 218, 231；
γ=4，β =111, 112, 114, 116, 128, 139, 158, 184, 188, 195, 203的新極端自對偶[68, 34, 12]碼。

致謝 (Acknowledgment) ………………………………………………………………………… i
摘要 (Abstract) ………………………………………………………………………………… ii
目錄 (Table of Contents) ……………………………………………………………………… iv
表目錄 (List of Tables) ……………………………………………………………………… v

第一章 緒論 (Introduction) ………………………………………………………………… 1

第二章 建構方法 (Construction Methods) ………………………………………………… 4
第2.1節 Kim[15]的定理………………………………………………………………………… 4
第2.2節 Kim的定理之演算……………………………………………………………………… 4
第2.3節 判斷兩個碼互不等價…………………………………………………………………… 4

第三章 應用 (Applications) ………………………………………………………………… 5
第3.1節 對應於W54,1，β =16與W54,2，β =21的不等價之極端自對偶[54, 27, 10]碼… 5
第3.2節 對應於W64,2，β =15的新極端自對偶[64, 32, 12]碼…………………………… 5
第3.3節 新極端自對偶[66, 33, 12]碼………………………………………………………… 6
第3.4節 新極端自對偶[68, 34, 12]碼………………………………………………………… 7

參考文獻 (References) ………………………………………………………………………… 12

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