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：我们提出了一种显式构造序列化速率为$1/2$的Wozencraft集合码（在任意固定有限域$\mathbb{F}_q$上）的方法，该码实现了最小距离$\Omega(\sqrt{k})$，其中$k$为消息长度。Wozencraft集合码的系数利用Sidon集和$\mathbb{F}_{q^{k}}$的循环结构构造，其中$k+1$为素数，且$q$是模$k+1$的原根。假设Artin猜想成立，对于任意素幂$q$，存在无穷多个这样的$k$。