Average-radius list-recoverability of random linear codes
Atri Rudra, Mary K. Wootters · Society for Industrial and Applied Mathematics eBooks · 2018
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles of arguments---which each work in their own parameter regimes but not in others---and moreover have left some gaps in our understanding of the list-decodability of random linear codes. In particular, none of these arguments work well for list-recovery, a generalization of list-decoding that has been useful in a variety of settings. In this work, we present a new approach, which works across parameter regimes and further generalizes to list-recovery. In particular, our argument provides better results for list-decoding and list-recovery over large fields; improved (quasipolynomial) list sizees for high-rate list-recovery of random linear codes; improved algorithmic results for list-decoding; and optimal average-radius list-decoding over constant-sized alphabets.