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arXiv · 2305.02484

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

Venkatesan Guruswami·Shilun Li
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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 $\mathbb{F}_q$) that achieve minimum distance $\Omega(\sqrt{k})$ where $k$ is the message length. The coefficients of the Wozencraft ensemble codes are constructed using Sidon Sets and the cyclic structure of $\mathbb{F}_{q^{k}}$ 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, Shilun Li. 2023-05-04. A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble. https://doi.org/10.1109/tit.2024.3510698

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