【23页精品】Combinatorial limitations of a strong form of list decoding

Abstract: We prove the following results concerning the combinatorics of list decoding,motivated by the exponential gap between the known upper bound (of$O(1/\gamma)$) and lower bound (of $\Omega_p(\log (1/\gamma))$) for thelist-size needed to decode up to radius $p$ with rate $\gamma$ away fromcapacity, i.e.,..