By Raaphorst et al, for a prime power $q$, covering arrays (CAs) with strength 3 and index 1, defined over the alphabet ${\mathbb{F}}_q$, were constructed using the output of linear feedback shift registers defined by cubic primitive polynomials in ${\mathbb{F}}_q\left[x\right]$. These arrays have $2q^3-1$ rows and $q^2+q+1$ columns. We generalize this construction to apply to all polynomials; provide a new proof that CAs are indeed produced; and analyze the parameters of the generated arrays. Besides arrays that match the parameters of those of Raaphorst et al, we obtain arrays matching some constructions that use Chateauneuf‐Kreher doubling; in both cases these are some of the best arrays currently known for certain parameters.

中文翻译：

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覆盖阵列构造的扩展

Raaphorst等人的文章 $q$，覆盖强度为3和索引为1的数组（CA），定义在字母上 ${\mathbb{F}}_q$，是由三次三次多项式定义的线性反馈移位寄存器的输出构造的 ${\mathbb{F}}_q\left[X\right]$。这些数组有$2q^3-\mathrm{1个}$ 行和 $q^2+q+\mathrm{1个}$列。我们将这种构造推广到所有多项式。提供确实产生了CA的新证据；并分析生成的数组的参数。除了与Raaphorst等人的参数匹配的数组外，我们还获得了与某些使用Chateauneuf-Kreher倍增的构造匹配的数组；在这两种情况下，这都是某些参数目前已知的最佳数组。