Optimal Cyclic Codes With Generalized Niho-Type Zeros and the Weight Distribution

Xiong Maosheng; Li Nian

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Optimal Cyclic Codes With Generalized Niho-Type Zeros and the Weight Distribution

机译：具有广义Niho型零点和权重分布的最佳循环码

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摘要

In this paper, we extend two earlier works further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are optimal and have only a few non-zero weights. Besides using similar ideas, we carry out some subtle manipulation of certain exponential sums.

机译：在本文中，我们在两个方向上进一步扩展了两个较早的工作，并在更宽松的条件下计算了这些循环码的权重分布。有趣的是，该系列中的许多循环码都是最优的，并且只有少数非零权重。除了使用类似的想法外，我们对某些指数和还进行了一些细微的操作。

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来源
《Information Theory, IEEE Transactions on》 |2015年第9期|4914-4922|共9页
作者
Xiong Maosheng; Li Nian;
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作者单位

Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Cyclic codes; Niho exponent; Vandermonde matrix; weight distribution;

机译：循环码;Niho指数;范德蒙矩阵;权重分布;

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专利

1. Weight distribution of cyclic codes with arbitrary number of generalized Niho type zeroes [J] . Xiong Maosheng, Li Nian, Zhou Zhengchun, Designs, Codes and Crytography . 2016,第3期

机译：具有任意数量的广义Niho类型零的循环码的权重分布
2. A family of optimal ternary cyclic codes from the Niho-type exponent [J] . Yan Haode, Zhou Zhengchun, Du Xiaoni Finite fields and their applications . 2018,第NOVa期

机译：Niho型指数的最佳三元循环码族
3. The Weight Distributions of the Duals of Cyclic Codes With Two Zeros [J] . Ding C., Liu Y., Ma C., Information Theory, IEEE Transactions on . 2011,第12期

机译：具有两个零的循环码对偶的权重分布
4. Generalized Hamming Weights of Cyclic Codes from Algebraic Function Fields [C] . Wanbao Hu, Xiaohong Fang International Conference on Materials Science and Information Technology . 2013

机译：代数函数字段的循环码的广义汉敏重量
5. GENERALIZED WEIGHTS FOR LINEAR CODES. [D] . GOLDBERG, DONALD YALE. 1978

机译：线性编码的广义权重。
6. Generalized weighted likelihood density estimators with application to finite mixture of exponential family distributions [O] . Tingting Zhan, Inna Chevoneva, Boris Iglewicz -1

机译：具有应用于指数家庭分布的有限混合物的广义加权似然密度估计
7. Weight Distributions of a Class of Cyclic Codes with Arbitrary Number of Zeros II [O] . Yang, Jing, Xia, Lingli, Xiong, Maosheng 2014

机译：一类具有任意数的循环码的权重分布零点二
8. Cyclic Codes. Research Program to Extend the Theory of Weight Distribution and Related Problems for Cyclic Error-Correcting Codes and Constructive Coding Theory [R] . Assmus, E. F., Mattson, H. F., Turyn, R. 1966

机译：循环码。扩展循环纠错码权重分布理论及相关问题的研究方案及构造编码理论

Optimal Cyclic Codes With Generalized Niho-Type Zeros and the Weight Distribution

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