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An extension of a construction of covering arrays
Author(s) -
Panario Daniel,
Saaltink Mark,
Stevens Brett,
Wevrick Daniel
Publication year - 2020
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21747
Subject(s) - mathematics , alphabet , extension (predicate logic) , combinatorics , row , matching (statistics) , discrete mathematics , computer science , statistics , philosophy , linguistics , database , programming language
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.