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QUALIFIED DIFFERENCE SETS FROM UNIONS OF CYCLOTOMIC CLASSES

Part of: Designs and configurations Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  17 April 2009

KEVIN BYARD  and
KEVIN BROUGHAN
KEVIN BYARD*
Affiliation:
Institute of Information and Mathematical Sciences, Massey University, Albany, North Shore, Auckland, New Zealand (email: [email protected])
KEVIN BROUGHAN
Affiliation:
Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Qualified difference sets (QDS) composed of unions of cyclotomic classes are discussed. An exhaustive computer search for such QDS and modified QDS that also possess the zero residue has been conducted for all powers n=4,6,8 and 10. Two new families were discovered in the case n=8 and some new isolated systems were discovered for n=6 and n=10.

Keywords

qualified residue difference setsdifference setscyclotomy

MSC classification

Secondary: 05B10: Difference sets (number-theoretic, group-theoretic, etc.) 11T22: Cyclotomy
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 1 , August 2009 , pp. 147 - 158
Copyright
Copyright © Australian Mathematical Society 2009

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