| 达到Gilbert-Varshamov界的准扭码 |
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| 引用本文： | 卢啸华,王永超,丁洋.达到Gilbert-Varshamov界的准扭码[J].上海大学学报(自然科学版),2021,27(2):289-297. |
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| 作者姓名： | 卢啸华 王永超 丁洋 |
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| 作者单位： | 上海大学 理学院, 上海 200444 |
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| 基金项目： | 国家自然科学基金资助项目(11671248) |
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| 摘 要： | 准扭码是循环码的一种推广,1-生成准扭码同构于多项式剩余类环的1-生成子模.Gilbert-Varshamov界是衡量准扭码好坏的一个重要标准.利用不可约多项式的性质得到任意的一个1-生成准扭码,有很大概率渐进达到Gilbert-Varshamov界.
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| 关 键 词： | 循环码 Gilbert-Varshamov界 不可约多项式 准扭码 |
| 收稿时间： | 2018-12-04 |
Quasi-twisted codes achieving the Gilbert-Varshamov bound |
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| LU Xiaohua,WANG Yongchao,DING Yang.Quasi-twisted codes achieving the Gilbert-Varshamov bound[J].Journal of Shanghai University(Natural Science),2021,27(2):289-297. |
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| Authors: | LU Xiaohua WANG Yongchao DING Yang |
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| Institution: | College of Sciences, Shanghai University, Shanghai 200444, China |
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| Abstract: | Quasi-twisted codes are regarded as a generalisation of cyclic codes. The Gilbert-Varshamov bound is an important criterion for measuring the quality of quasi-twisted codes. A class of randomized one-generator quasi-twisted codes was presented. Furthermore, it was proved that, using the properties of irreducible polynomials, random one-generator quasi-twisted codes asymptotically achieved the Gilbert-Varshamov bound with high probability and identified a one-generator module of a polynomial quotient ring. |
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| Keywords: | cyclic codes Gilbert-Varshamov bound irreducible polynomials quasi-twisted codes |
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