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 $q$.
Categories: cs.IT math.CO math.IT