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

05/04/2023

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by   Venkatesan Guruswami, et al.

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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.