Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
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DOI：
10.1016/j.disc.2021.112718
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发表时间：
2018-04
期刊：
影响因子：
--
通讯作者：
Fei Li;Xiumei Li
中科院分区：
文献类型：
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作者：
Fei Li;Xiumei Li
线性码的权族由于其重要的理论价值和密码学应用价值而成为密码学研究的热点。本文将奇特征有限域上的退化二次型限制在子空间中，并引入与退化二次型有关的商空间。从商空间上的多项式导出了一个非退化二次型。得到了关于子空间和商空间的一些相关结果。在此基础上，确定了与之相关的一类线性码的权族。
Weight hierarchies of linear codes have been an interesting topic due to their important values in theory and applications in cryptography. In this paper, we restrict a degenerate quadratic formfover a finite field of odd characteristic to subspaces and introduce a quotient space related to the degenerate quadratic formf. From the polynomialfover the quotient space, a non-degenerate quadratic form is induced. Some related results on the subspaces and quotient spaces are obtained. Based on these results, the weight hierarchies of a family of linear codes related tofare determined.