An extension of a construction of covering arrays. Issue 11 (4th August 2020) - Panario, Daniel; Saaltink, Mark; Stevens, Brett; Wevrick, Daniel
Abstract: By Raaphorst et al, for a prime power q, covering arrays (CAs) with strength 3 and index 1, defined over the alphabet F q, were constructed using the output of linear feedback shift registers defined by cubic primitive polynomials in F q [ x ] . These arrays have 2 q 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.