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

Authors Venkatesan Guruswami , Shilun Li

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Author Details

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

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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)


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.

Subject Classification

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


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