Abstract:In this work, we prove new results concerning the combinatorial properties of random linear codes. By applying the thresholds framework from Mosheiff et al. (FOCS 2020) we derive fine-grained results concerning the list-decodability and -recoverability of random linear codes.Firstly, we prove a lower bound on the list-size required for random linear codes over Fq ε-close to capacity to list-recover with error radius ρ and input lists of size ℓ. We show that the list-size, where R is the rate of the random lin… Show more
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