2019代数编码系列报告之六——刘宏伟教授学术报告

发布时间:2019-07-26

报告题目:Galois Hulls of Linear Codes over Finite Fields

  人:刘宏伟 教授(华中师范大学

报告时间:2019731号(周三)下午16:30

报告地点:磬苑校区数学科学学院H306

报告摘要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

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2019年7月26日

 

 


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