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 $q$.

翻译：我们给出了一种显式构造，用于生成一系列码率为$1/2$的Wozencraft系码（定义在任意固定有限域$\mathbb{F}_q$上），其最小距离达到$\Omega(\sqrt{k})$，其中$k$为消息长度。该Wozencraft系码的系数利用Sidon集以及$\mathbb{F}_{q^{k}}$的循环结构构造，此时$k+1$为素数且$q$是模$k+1$的本原根。若假定Artin猜想成立，则对于任意素幂$q$，存在无穷多个满足条件的$k$。