An extension of a construction of covering arrays

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.