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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