Roth-Lempel NMDS Codes of Non-Elliptic-Curve Type

讲座时间 Datetime: 2023年6月13日，星期二，15:00 – 16:30

地点 Venue: 腾讯会议：484-192-366

报告人 Speaker: 韩冬春 副教授

单位 Affiliation: 西南交通大学

主持人Host：张汉斌 助理教授

报告摘要 Abstract:

NMDS codes correspond to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. There have been many constructions of NMDS codes, but most of them are focus on fixed q or k, except for constructions from elliptic curves. Roth and Lempel (IEEE Trans. Inf. Theory 1989) constructed a type of linear codes (referred as Roth-Lempel codes), and presented the necessary and sufficient conditions of Roth-Lempel code to be MDS. Especially, they pointed out that the resultant MDS codes is not linearly equivalent to Reed-Solomon codes. In this talk, the NMDS properties of Roth-Lempel codes will be analyzed. We also obtain the necessary and sufficient condition of Roth-Lempel codes to be NMDS, and further completely determine the weight distributions of Roth-Lempel codes with length q+2. Most notably, we illustrate the linearly inequivalence of Roth-Lempel NMDS codes and elliptic curve NMDS codes.

报告人简介：

韩冬春，西南交通大学数学学院副教授，硕士研究生导师，西南交通大学雏鹰学者。2015年于南开大学组合数学中心获得理学博士学位。研究方向为组合，数论，编码及其交叉领域，并在相关领域著名杂志J. Combin. Theory Ser. A，SIAM J. Discrete Math.，J. Number Theory，IEEE Trans. Inform. Theory等发表论文20余篇。主持国家自然科学基金青年基金、面上项目、四川省科技厅项目和成都市科技厅项目各一项。