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

Authors Venkatesan Guruswami , Shilun Li

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ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
  • Theory of computation → Error-correcting codes
Keywords
  • Algebraic codes
  • Pseudorandomness
  • Explicit Construction
  • Wozencraft Ensemble
  • Sidon Sets

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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) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.50

Author Details

Venkatesan Guruswami
  • Department of EECS, University of California, Berkeley, CA, USA
Shilun Li
  • Department of Mathematics, University of California, Berkeley, CA, USA

Funding

  • Guruswami, Venkatesan: Research supported by a Simons Investigator Award and NSF grants CCF-2210823 and CCF-2228287.
  • Li, Shilun: Research supported by University of California, Berkeley under Berkeley Fellowship.

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