@article{0f94758be03f4401bb8a60aa75692b92,
title = "GENERALIZED SINGLETON BOUND AND LIST-DECODING REED-SOLOMON CODES BEYOND THE JOHNSON RADIUS",
abstract = "In this paper we take a combinatorial approach to the problem of list-decoding, which allows us to determine the precise relation (up to the exact constant) between the decoding radius, list size, and code rate. We prove a generalized Singleton bound for a given list size, and conjecture that the bound is tight for most Reed-Solomon (RS) codes over large enough finite fields. We also show that the conjecture holds true for list sizes 2 and 3, and as a by product show that most RS codes with a rate of at least 1/9 are list-decodable beyond the Johnson radius. Last, we give the first explicit construction in the literature of such RS codes. The main tools used in the proof are a new type of linear dependency between codewords of a code that are contained in a small Hamming ball, and a surprising connection between list-decoding and the notion of cycle space in graph theory. Both of them are new, and may be of independent interest.",
keywords = "Johnson radius, Reed-Solomon codes, generalized Singleton bound, list-decoding",
author = "Chong Shangguan and Itzhak Tamo",
note = "Publisher Copyright: {\textcopyright} 2023 Society for Industrial and Applied Mathematics.",
year = "2023",
month = jun,
doi = "10.1137/20M138795X",
language = "אנגלית",
volume = "52",
pages = "684--717",
journal = "SIAM Journal on Computing",
issn = "0097-5397",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "3",
}