2026-07-26T03:03:06Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18875 2024-03-06T11:02:48Z ddc:004 open_access

A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble Guruswami, Venkatesan Li, Shilun Algebraic codes Pseudorandomness Explicit Construction Wozencraft Ensemble Sidon Sets 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Venkatesan Guruswami and Shilun Li 2023 Is Part Of LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2023.50 urn:nbn:de:0030-drops-188751 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.50 eng https://creativecommons.org/licenses/by/4.0/legalcode