License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.50
URN: urn:nbn:de:0030-drops-188751
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18875/
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Guruswami, Venkatesan ; Li, Shilun

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

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LIPIcs-APPROX50.pdf (0.7 MB)

Abstract

We present an explicit construction of a sequence of rate 1/2 Wozencraft ensemble codes (over any fixed finite field ?_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 ?_{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.

BibTeX - Entry

@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/opus/volltexte/2023/18875},
  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}
}

Keywords: Algebraic codes, Pseudorandomness, Explicit Construction, Wozencraft Ensemble, Sidon Sets
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)
Issue Date: 2023
Date of publication: 04.09.2023

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