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Rank-Metric Codes and Related Topics

主 讲 人 :周悦    副研究员

活动时间:12月15日14时30分    

地      点 :腾讯会议(会议ID:582910414,密码1215)

讲座内容:

Let K be a field. For any two m by n matrices A, B overK, the rank metric is

defined by d(A, B) = rank(A- B). A rank-metric code Cis just a subset of m

by n matrices over K, and its minimum distance isdefined by d(C)=min{d(A,B)}, where A,B is in C and A is not equal to B. Thereare several interesting research topics in finite geometry, cryptography andcoding theory, which can be equivalently described in the context of rank-metriccodes. In this talk, we first give a brief introduction of their motivationsand applications in network coding theory. Then we concentrate on the so-calledmaximum rank distance (MRD) codes over finite fields, which were firstinvestigated by Delsarte (1978) in the context of association schemes ofbilinear forms over finite fields. We summarize known constructions of MRDcodes and look at their

equivalence problem. The connections between MRD codesand several other

objects such as semifields, Moore determinants, andscattered linear sets will

also be mentioned. Finally, we turn to rank-metriccodes over symmetric, and

Hermitian bilinear forms.


主讲人介绍:

周悦,国防科技大学数学系副研究员。主要研究有限几何、代数组合及其在编码密码中的应用。在Adv. Math, Journal ofCryptology, JCTA等期刊发表相关论文40篇。2016年获得“国际组合及其应用学会”Kirkman奖章。2019年起担任国际期刊Designs, Codes and Cryptography的编委。

发布时间:2020-12-13 08:44:39

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