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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.50

A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble

Authors: Venkatesan Guruswami and Shilun Li

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract

We present an explicit construction of a sequence of rate 1/2 Wozencraft ensemble codes (over any fixed finite field 𝔽_q) that achieve minimum distance Ω(√k) where k is the message length. The coefficients of the Wozencraft ensemble codes are constructed using Sidon Sets and the cyclic structure of 𝔽_{q^k} where k+1 is prime with q a primitive root modulo k+1. Assuming Artin’s conjecture, there are infinitely many such k for any prime power q.

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Venkatesan Guruswami and Shilun Li. A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 50:1-50:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{guruswami_et_al:LIPIcs.APPROX/RANDOM.2023.50,
  author =	{Guruswami, Venkatesan and Li, Shilun},
  title =	{{A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{50:1--50:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.50},
  URN =		{urn:nbn:de:0030-drops-188751},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.50},
  annote =	{Keywords: Algebraic codes, Pseudorandomness, Explicit Construction, Wozencraft Ensemble, Sidon Sets}
}

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A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble

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