Year: 2024
Type: article
Abstract: We present an explicit construction of a sequence of rate$1/2$Wozencraft ensemble codes (over any fixed prime 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 q.
Authors: Venkatesan Guruswami, Shilun Li
Institution: University of California, Berkeley
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405023173