报告题目：Galois Hulls of Linear Codes over Finite Fields
报 告 人：刘宏伟 教授（华中师范大学）
报告时间：2019年7月31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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科学技术处
2019年7月26日