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Speaker:Yuan Chen, Associate Professor, Shanghai Jiao Tong University
Date:September 24, 2022
Sponsor:Research Center for Mathematics and Interdisciplinary Sciences
Research Center for Nonlinear Expectation
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.
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