An extension of a construction of covering arrays. Issue 11 (4th August 2020)

• Record Type: Journal Article
• Authors: Panario, Daniel; Saaltink, Mark; Stevens, Brett; Wevrick, Daniel
• Is Part Of: Journal of combinatorial designs. Volume 28:Issue 11(2020:Nov.)
• Page Start: 842
• Page End: 861
• Publication Date: 2020-08-04
• Subjects: covering array -- covering perfect hash family -- finite field -- primitive polynomial -- pseudo‐order; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21747
• Languages: English
• ISSNs: 1063-8539

Abstract

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.