## 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).

Original language | English |
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Title of host publication | STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Samir Khuller, Virginia Vassilevska Williams |

Publisher | Association for Computing Machinery |

Pages | 1479-1488 |

Number of pages | 10 |

ISBN (Electronic) | 9781450380539 |

DOIs | |

State | Published - 15 Jun 2021 |

Externally published | Yes |

Event | 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy Duration: 21 Jun 2021 → 25 Jun 2021 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Conference

Conference | 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 |
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Country/Territory | Italy |

City | Virtual, Online |

Period | 21/06/21 → 25/06/21 |

### Bibliographical note

Publisher Copyright:© 2021 ACM.

### Funding

∗Research partially supported by ISF grant 1724/15. †The research leading to these results has received funding from the Israel Science Foundation (grant number 552/16) and from the Len Blavatnik and the Blavatnik Family foundation.

Funders | Funder number |
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Blavatnik Family Foundation | |

Israel Science Foundation | 552/16, 1724/15 |

## Keywords

- Reed - Muller codes
- capacity-achieving codes
- weight enumerator