20190701
A General Construction of Ordered Orthogonal Arrays Using LFSRs
Publication
Publication
IEEE Transactions on Information Theory , Volume 65  Issue 7 p. 4316 4326
The q^{t} \times (q+1)t ordered orthogonal arrays (OOAs) of strength t over the alphabet \mathbb {F}{q} were constructed using linear feedback shift register sequences (LFSRs) defined by primitive polynomials in \mathbb {F}{q}[x]. In this paper, we extend this result to all polynomials in \mathbb {F}{q}[x] which satisfy some fairly simple restrictions, i.e., the restrictions that are automatically satisfied by primitive polynomials. While these restrictions sometimes reduce the number of columns produced from (q+1)t to a smaller multiple of t , in many cases, we still obtain the maximum number of columns in the constructed OOA when using nonprimitive polynomials. For 2 \le q \le 9 and small t , we generate OOAs in this manner for all permissible polynomials of degree t in \mathbb {F}{q}[x] and compare the results to the ones produced in [2], [16], and [17] showing how close the arrays are to being 'full' orthogonal arrays. Unusually for the finite fields, our arrays based on the nonprimitive irreducible and even reducible polynomials are closer to the orthogonal arrays than those built from the primitive polynomials.
Additional Metadata  

(t, m, s)nets, linear feedback shift registers, Ordered orthogonal arrays  
doi.org/10.1109/TIT.2019.2894660  
IEEE Transactions on Information Theory  
Organisation  School of Mathematics and Statistics 
Panario, D, Saaltink, M. (Mark), Stevens, B, & Wevrick, D. (Daniel). (2019). A General Construction of Ordered Orthogonal Arrays Using LFSRs. IEEE Transactions on Information Theory, 65(7), 4316–4326. doi:10.1109/TIT.2019.2894660
