The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs

Li S.; Hu S.; Feng T.; Ge G.

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The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs

机译：与厄米形式图有关的一类循环码的权重分布

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摘要

The determination of weight distribution of cyclic codes involves the evaluation of Gauss sums and exponential sums. Despite some cases where a neat expression is available, the computation is generally rather complicated. In this note, we determine the weight distribution of a class of reducible cyclic codes whose dual codes may have arbitrarily many zeros. This goal is achieved by building an unexpected connection between the corresponding exponential sums and the spectra of Hermitian forms graphs.

机译：循环码权重分布的确定涉及对高斯和和指数和的评估。尽管在某些情况下可以使用整洁的表达式，但计算通常相当复杂。在本说明中，我们确定了一类可归约循环码的权重分布，其对偶码可能具有任意多个零。通过在相应的指数和与Hermitian形式图的光谱之间建立意外连接来实现此目标。

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来源
《Information Theory, IEEE Transactions on》 |2013年第5期|3064-3067|共4页
作者
Li S.; Hu S.; Feng T.; Ge G.;
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作者单位

Department of Mathematics, Zhejiang University, Hangzhou, P. R. China;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Cryptography; Educational institutions; Eigenvalues and eigenfunctions; Hamming weight; Polynomials; Cayley graphs; Hermitian forms graphs; cyclic codes; weight distribution;

机译：密码学;教育机构;特征值和特征函数;汉明重量;多项式Cayley图;厄米形式的图形;循环码;体重分布;

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机译：1与Hermitian形式图相关的一类循环码的权重分布

The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs

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