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# 2019代數編碼系列報告之六——劉宏偉教授學術報告

發布時間：2019-07-26作者：訪問量：11

報告題目：Galois Hulls of Linear Codes over Finite Fields

人：劉宏偉 教授（華中師范大學

報告時間：2019731號（周三）下午16:30

報告地點：磬苑校區數學科學學院H306

報告摘要In this talk, we show that the dimension of the $\ell$-Galois hull of a linear code is invariant under permutation equivalences and we provide a method to calculate the dimension of the $\ell$-Galois hull through a generator matrix of the code. Moreover, we obtain that the dimension of the $\ell$-Galois hull of a ternary code is also invariant under monomial equivalences. We show that every $[n,k]$ linear code over $\mathbb F_{q}$ is monomial equivalent to an $\ell$-Galois LCD code for any $q>4$. We conclude that if there exists an $[n,k]$ linear code over $\mathbb F_{q}$ for any $q>4$, then there exists an $\ell$-Galois LCD code with the same parameters for any $0\le \ell\le e-1$, where $q=p^e$ for some prime number $p$. As an application, we characterize the $\ell$-Galois hulls of matrix product codes over finite fields

歡迎各位老師、同學屆時前往！

科學技術處

2019年7月26日

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