@inproceedings{19e4bff0a1354f939f08811485c62a90,
title = "On codes decoding a constant fraction of errors on the BSC",
abstract = "We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is successful on the BEC can also decode over a range of binary memoryless symmetric (BMS) channels. In particular, applying the result of Kudekar, Kumar, Mondelli, Pfister, ?a?o?lu and Urbanke from STOC 2016, we prove that a Reed-Muller code of positive rate R decodes errors on the p with high probability if p < 1/2 - ?2-R(1-2-R).",
keywords = "Reed - Muller codes, capacity-achieving codes, weight enumerator",
author = "Jan H{\c a}z{\l}a and Alex Samorodnitsky and Ori Sberlo",
note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 ; Conference date: 21-06-2021 Through 25-06-2021",
year = "2021",
month = jun,
day = "15",
doi = "10.1145/3406325.3451015",
language = "الإنجليزيّة",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
publisher = "Association for Computing Machinery",
pages = "1479--1488",
editor = "Samir Khuller and Williams, {Virginia Vassilevska}",
booktitle = "STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing",
address = "الولايات المتّحدة",
}