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.
@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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