【学术报告】On Linear Codes Whose Hermitian Hulls are MDS

报告人：罗高骏（南京航空航天大学）

时 间：2024年12月6日11:00

地 点：厦门大学海韵园实验楼S102

内容摘要:

Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have been utilized as ingredients to construct entanglement-assisted quantum error correcting codes. This family of quantum codes is often seen as a generalization of quantum stabilizer codes. Theoretically, compared with the Euclidean setup, the Hermitian case is much harder to deal with. Hermitian hulls of MDS linear codes with low dimensions have been explored, mostly from generalized Reed-Solomon codes. Characterizing Hermitian hulls which themselves are MDS appears to be more involved and has not been extensively studied. This paper introduces some tools to study linear codes whose Hermitian hulls are MDS. Using the tools, we then propose explicit constructions of such codes. We consider Hermitian hulls of linear MDS codes. We demonstrate that, given the same Hermitian hull dimensions, the codes from our constructions.

个人简介：

罗高骏，南京航空航天大学副研究员。2019年博士毕业于南京航空航天大学，2021年至2024年于新加坡南洋理工大学从事博士后研究工作。主要研究方向为代数编码理论、序列设计与量子信息。近五年，以第一/通讯作者发表SCI检索论文20余篇，包括IEEE Trans系列10篇。主持国家自然科学基金青年基金一项，江苏省自然科学基金青年基金一项，曾获得江苏省科学技术奖。2022年至今，担任期刊COAM（《Computational and Applied Mathematics》）的Associate Editor。

联系人：祝辉林