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A technique for constructing non‐embeddable quasi‐residual designs
Author(s) -
Ionin Yury J.,
MackenzieFleming Kirsten
Publication year - 2002
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.900
Subject(s) - mathematics , combinatorics , integer (computer science) , prime (order theory) , residual , prime power , construct (python library) , hadamard transform , hadamard matrix , combinatorial design , discrete mathematics , algorithm , computer science , mathematical analysis , programming language
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