The weight distributions of a class of cyclic codes
The weight distributions of a class of cyclic codes
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DOI：
10.1016/j.ffa.2012.06.001
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发表时间：
2011-11
期刊：
影响因子：
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通讯作者：
Maosheng Xiong
中科院分区：
文献类型：
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作者：
Maosheng Xiong
最近，Ma 等人在几种情况下获得了具有两个零的循环码的对偶的权重分布。 （2011）[14]，丁等人。 (2011) [5]，王等人。 （2011）[20]。在本文中，我们针对一般问题提供了一种略有不同的方法，并用它来解决一个更特殊的情况。我们广泛使用数论中的标准工具，例如有限域特征、高斯和和雅可比和，将求权重分布的问题转化为计算有限域上某些特征和的问题，在特殊情况下与计算有限域上某些椭圆曲线上的点数有关。其他情况也可以通过此方法进行。
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases in Ma et al. (2011) [14], Ding et al. (2011) [5], Wang et al. (2011) [20]. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special case. We make extensive use of standard tools in number theory such as characters of finite fields, the Gauss sums and the Jacobi sums to transform the problem of finding the weight distribution into a problem of evaluating certain character sums over finite fields, which on the special case is related with counting the number of points on some elliptic curves over finite fields. Other cases are also possible by this method.