| 有19-(4,f)型自同构的二元自对偶码 |
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| 引用本文： | 王荣,王俊新.有19-(4,f)型自同构的二元自对偶码[J].计算机工程与科学,2015,37(9):1661-1666. |
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| 作者姓名： | 王荣 王俊新 |
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| 作者单位： | ;1.山西财经大学应用数学学院 |
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| 基金项目： | 国家自然科学基金资助项目（70973072，70573066）;山西财经大学青年科研基金资助项目(晋财大校［2014］90号) |
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| 摘 要： | 应用二元自对偶码可看成几个自对偶码的直和理论,研究了具有19-(4,f)型自同构、码长在100以内的的二元自对偶码。这种对偶码都可看成一个码长为4的收缩码和GF(2)n上一些偶重量多项式的直和。证明了码长大于80且小于100时,不存在19-(4,f)型的二元自对偶码。根据码长较短的自对偶码分别构造出了码长为76、78和80的二元自对偶码,并给出其生成矩阵。由码的等价得到了这几类码可能的分类情况。运行Matlab程序,证明了具有19-(4,2)型和19-(4,4)型的二元自对偶码在等价情况下都有11个,19-(4,0)型的二元自对偶码在等价情况下是不存在的。
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| 关 键 词： | 自对偶码 生成矩阵 自同构 等价 |
| 收稿时间： | 2014-12-17 |
| 修稿时间： | 2015-09-25 |
Binary self-dual codes with 19-(4,f) automorphism |
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| WANG Rong,WANG Jun xin.Binary self-dual codes with 19-(4,f) automorphism[J].Computer Engineering & Science,2015,37(9):1661-1666. |
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| Authors: | WANG Rong WANG Jun xin |
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| Affiliation: | (College of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006,China ) |
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| Abstract: | We discuss the binary self dual codes of length 76 and 100 with automorphism of order 19. These binary self dual codes can be seen as a direct sum of contract code of length 4 and some even weight polynomials over GF(2)n. We prove that self dual codes of length between 80 and 100 do not exist. We also construct the binary self dual codes of length 76, 78 and 80 through the shorter self dual codes respectively, and present their generator matrices. Simulations in Matlab prove that under the condition of equivalence, there are 11 binary self dual codes of 19 (4, 2) and 19 (4,4) types, whereas binary self dual codes of 19 (4, 0) type do not exist. |
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| Keywords: | self-dual codes generator matrix automorphism equivalence |
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