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Infinite families of non‐embeddable quasi‐residual Menon designs
Author(s) -
Alraqad Tariq,
Shrikhande Mohan
Publication year - 2009
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.20192
Subject(s) - residual , mathematics , combinatorics , combinatorial design , hadamard transform , order (exchange) , algorithm , mathematical analysis , finance , economics
A Menon design of order h 2 is a symmetric (4 h 2 ,2 h 2 ‐ h , h 2 ‐ h )‐design. Quasi‐residual and quasi‐derived designs of a Menon design have parameters 2‐(2 h 2 + h , h 2 , h 2 ‐ h ) and 2‐(2 h 2 ‐ h , h 2 ‐ h , h 2 ‐ h ‐1), respectively. In this article, regular Hadamard matrices are used to construct non‐embeddable quasi‐residual and quasi‐derived Menon designs. As applications, we construct the first two new infinite families of non‐embeddable quasi‐residual and quasi‐derived Menon designs. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 53–62, 2009