New Near-Linear Time Decodable Codes Closer to the GV Bound

Guy Blanc, Dean Doron

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We construct a family of binary codes of relative distance 1/2 − ε and rate ε2 · 2− logα(1/ε) for α ≈ 1/2 that are decodable, probabilistically, in near-linear time. This improves upon the rate of the state-of-the-art near-linear time decoding near the GV bound due to Jeronimo, Srivastava, and Tulsiani, who gave a randomized decoding of Ta-Shma codes with α ≈ 5/6 [34, 20]. Each code in our family can be constructed in probabilistic polynomial time, or deterministic polynomial time given sufficiently good explicit 3-uniform hypergraphs. Our construction is based on a new graph-based bias amplification method. While previous works start with some base code of relative distance 1/2 − ε0 for ε0 ≫ ε and amplify the distance to 1/2 − ε by walking on an expander, or on a carefully tailored product of expanders, we walk over very sparse, highly mixing, hypergraphs. Study of such hypergraphs further offers an avenue toward achieving rate Ω(ε2). For our unique- and list-decoding algorithms, we employ the framework developed in [20].

Original languageEnglish
Title of host publication37th Computational Complexity Conference, CCC 2022
EditorsShachar Lovett
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772419
StatePublished - 1 Jul 2022
Event37th Computational Complexity Conference, CCC 2022 - Philadelphia, United States
Duration: 20 Jul 202223 Jul 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference37th Computational Complexity Conference, CCC 2022
Country/TerritoryUnited States


  • Unique decoding
  • expander walks
  • hypergraphs
  • list decoding
  • small-bias sample spaces
  • the Gilbert–Varshamov bound

ASJC Scopus subject areas

  • Software


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