Weight Distributions of a Class of Cyclic Codes with Arbitrary Number of Zeros II
Weight Distributions of a Class of Cyclic Codes with Arbitrary Number of Zeros II
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发表时间：
2014-05
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通讯作者：
Jing Yang;Lingli Xia;Maosheng Xiong
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作者：
Jing Yang;Lingli Xia;Maosheng Xiong
循环码是一类重要的线性码，其码重分布已被广泛研究。到目前为止，已有的结果大多是针对零不超过三个的循环码。最近，\cite{Y-X-D12}构造了一类具有任意个零的循环码，并计算了几种情况下的权重分布。在本文中，我们确定了一个新的家庭这样的码的重量分布。这是通过某些新的方法，如有限域上的Jacobi和理论和一些复杂的组合恒等式的微妙处理来实现的。
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12} constructed a class of cyclic codes with arbitrary number of zeros, and computed the weight distributions for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.