Weight Distributions of a Class of Cyclic Codes with Arbitrary Number of Nonzeros in Quadratic Case

Jing Yang Department of Mathematical Sciences, Tsinghua University Maosheng Xiong Department of Mathematics, The Hong Kong University of Science andTechnology LingliXia Basic Courses Department, Beijing Union University

Number Theory mathscidoc:1612.24001

Finite Fields and Their Applications, 36, 41-62, 2015
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 nonzeros. Recently, the authors of [37]constructed a class of cyclic codes with arbitrary number of nonzeros, and computed the weight distribution for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by introducing certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.
Cyclic codes, Weight distribution, Gaussian periods, Jacobi sums
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@inproceedings{jing2015weight,
  title={Weight Distributions of a Class of Cyclic Codes with Arbitrary Number of Nonzeros in Quadratic Case},
  author={Jing Yang, Maosheng Xiong, and LingliXia},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161209114739744416683},
  booktitle={Finite Fields and Their Applications},
  volume={36},
  pages={41-62},
  year={2015},
}
Jing Yang, Maosheng Xiong, and LingliXia. Weight Distributions of a Class of Cyclic Codes with Arbitrary Number of Nonzeros in Quadratic Case. 2015. Vol. 36. In Finite Fields and Their Applications. pp.41-62. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161209114739744416683.
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