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

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.