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A technique for constructing non-embeddable quasi-residual designs

✍ Scribed by Yury J. Ionin; Kirsten Mackenzie-Fleming

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
134 KB
Volume
10
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

We propose a technique for constructing two infinite families of non‐embeddable quasi‐residual designs as soon as one such design satisfying certain conditions exists. The main tools are generalized Hadamard matrices and balanced generalized weighing matrices. Starting with a specific non‐embeddable quasi‐residual 2‐(27,9,4) design, we construct for every positive integer m a non‐embeddable 2‐(3^m^,3^m−1^,(3^m−1^−1)/2)‐design, and, if r~m~=(3^m^−1)/2 is a prime power, we construct for every positive integer n a non‐embeddable $2-(3^m(r^n_m-1)/(r_m-1), 3^{m-1}r^{n-1}_m, (3^{m-1}-1)r^{n-1}_m/2)$ design. For each design in these families, a symmetric design with the corresponding parameters is known to exist. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 160–172, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.900

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