On List Recovery of High-Rate Tensor Codes

We continue the study of list recovery properties high-rate tensor codes, initiated by Hemenway, Ron-Zewi, and Wootters (FOCS'17). In that work it was shown product an efficient (poly-time) globally recoverable code is approximately locally recoverable, as well in probabilistic near-linear time. This used turn to give first capacity-achieving decodable codes with (1) local decoding algorithms, (2) time global algorithms. also yielded constant-rate approaching Gilbert-Varshamov bound unique current we obtain following results: 1) The deterministic yields It gives 2) If base additionally correctable, then (genuinely) recoverable. (non-explicit) are correctable query complexity running N o (1). improves over prior Gopi et. al. (SODA'17; IEEE Transactions on Information Theory'18) only gave NE rate exponentially small 1/ε. 3) A nearly-tight combinatori allower output size for recovering codes. implies a lower xmlns:xlink="http://www.w3.org/1999/xlink">Ω(1/ xmlns:xlink="http://www.w3.org/1999/xlink">log xmlns:xlink="http://www.w3.org/1999/xlink">N)