Speaker:Li Nian, Professor, doctoral supervisor, Hubei University

Date:October 8, 2022

Time:10:00-11:00

Location:Tencent Meeting

Sponsor:School of Mathematics, Shandong University

Abstract:

Linear codes have a wide range of applications in the data storage systems, communication systems and consumer electronics products. In this talk, we present four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including infinite families of (near) Griesmer codes. We characterize the optimality of these four families of linear codes with an explicit computable criterion using the Griesmer bound and obtain many distanceoptimal linear codes. In addition, by a more in-depth discussion on some special cases of these four families of linear codes, we obtain several classes of (distance-)optimal linear codes with few weights and completely determine their weight distributions. We also show that most of our linear codes are self-orthogonal or minimal which are useful in applications.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/169630.htm