List-Decodability With Large Radius for Reed-Solomon Codes

List-decodability of Reed–Solomon codes has received a lot attention, but the best-possible dependence between parameters is still not well-understood. In this work, we focus on case where list-decoding radius form $r=1-\varepsilon $ for notation="LaTeX">$\varepsilon tending to zero. Our main result states that there exist with rate notation="LaTeX">$\Omega (\varepsilon)$ which are notation="LaTeX">$(1-\varepsilon, O(1/\varepsilon))$ -list-decodable, meaning any Hamming ball notation="LaTeX">$1-\varepsilon contains at most notation="LaTeX">$O(1/\varepsilon)$ codewords. This trade-off and code list size less than exponential in block length. By achieving improve recent Guo, Li, Shangguan, Tamo, Wootters, resolve motivating question their work. Moreover, while requires field be exponentially large length, only need polynomially (and fact, almost-linear suffices). We deduce our from more general theorem, prove good list-decodability properties random puncturings given very distance.