$\sigma-$ LCD codes over finite chain rings

发布时间：2023-04-11 作者：浏览次数：

Speaker:	刘修生教授	DateTime:	2023年4月15日（周六）下午：15:00-16:00
Brief Introduction to Speaker: 刘修生，男，教授。享受湖北省政府专项津贴，黄石市有突出贡献专家。中国计算机数学分会委员、湖北省数学学会理事、湖北省计算数学学会常务理事、湖北省工业与应用数学学会理事。武汉理工大学、武汉纺织大学和湖北师范大学学院硕士生兼职导师。已在Designs, Codes and Cryptography，Finite Fields and Their Applications，Discrete Mathematics 和Quantum Information Processing等SCI期刊发表系列学术论文60余篇，主编教材8部。主要研究方向：群与代数编码，多重线性代数。		Place:	6号楼二楼学术报告厅
Abstract:In this work, we first generalize the $\sigma$-LCD codes over finite fields to $\sigma$-LCD codes over finite chain rings. Under suitable conditions, linear codes over finite chain rings that are $\sigma$-LCD codes are characterized. Then we provide a necessary and sufficient condition for free constacyclic codes over finite chain rings to be $\sigma$-LCD. We also get some new binary LCD codes of different lengths which come from Gray images of constacyclic $\sigma$-LCD codes over $\mathbb{F}_2+\gamma\mathbb{F}_2+\gamma^2\mathbb{F}_2$. Finally, for special finite chain rings $\mathbb{F}_q+\gamma\mathbb{F}_q$, we define a new Gray map $\Phi$ from $(\mathbb{F}_q+\gamma\mathbb{F}_q)^n$ to $\mathbb{F}_q^{2n}$, and by using $\sigma$-LCD codes over finite chain rings $\mathbb{F}_{q}+\gamma\mathbb{F}_q$, we construct new entanglement-assisted quantum error-correcting (abbreviated to EAQEC) codes with maximal entanglement and parts of them are MDS EAQEC codes.

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