一、报告题目

New Bounds for Thresholds of Code Ensembles

二、主讲人

袁 晨

三、报告时间

2022年09月24日 16:30-17:30

四、报告地点

ZOOM会议号

五、摘要

I will first present some background for the threshold rate of random code and random linear code. After this, I will prove new results concerning combinatorial properties of random linear codes. By applying the thresholds framework from Mosheiff et al (FOCS 2020)，I will derive fine-grained results concerning the list-decodability and -recoverability of random linear codes. The first result is a lower bound on the list-size required for random linear codes over Fq ε-close to capacity. This is analogous to a lower bound for list-decoding that was recently obtained by Mosheiff et al (RANDOM 2020). Then, I will provide other results about list-decoding with constant list-sizes. Specifically, A tight upper and lower bounds were obtained on the rate required for binary random linear code of list size 3 and 4 and q-ary random linear code of list size 2.

六、主讲人简介

Chen Yuan obtained his PhD degree from Nanyang Technological University. Then, He worked as a postdoc in CWI for almost three years. After that, he joined Shanghai Jiao Tong University as an associate professor. His research interests include secure multiparty computation, secret sharing , coding theory and its application in theoretical computer science.He published over 20 papers in top journals and conferences such as IEEE TIT, TAMS, CRYPTO, EUROCRYPT, SODA, ICALP, ASIACRYPT, TCC and so on.

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心