Hostname: page-component-5c6d5d7d68-wp2c8 Total loading time: 0 Render date: 2024-08-08T07:38:07.364Z Has data issue: false hasContentIssue false
  • English
  • Français

A construction for certain classes of supplementary difference sets

Published online by Cambridge University Press:  09 April 2009

Joan Cooper
Joan Cooper
Affiliation:
Mathematics Department, University of NewcastleNewcastle, N.S.W. 2308Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let ν = ef + 1 be a prime power, and consider G the cyclic group of order ν − 1 with e cosets Ci, of order f defined as Ci = {xej+i: 0 ≦ j ≦ f − 1} and 0 ≦ i ≦ e − 1, where x is a primitive element of GF(pα) and a generator of G. By using these cosets we give a simple construction for certain classes of Supplementary Difference Sets, Difference Sets, and Szekeres Difference Sets. These classes are not new, but the simple method of construction is original.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 182 - 187
Copyright
Copyright © Australian Mathematical Society 1976

References

Cooper, Joan and Wallis, Jennifer (1972), ‘A construction for Hadamard arrays’, Bull. Austral. Math. Soc. 7, 269–278.CrossRefGoogle Scholar
Cooper, Joan (1972), ‘A binary composition for collections and sets’, (Proceedings of the First Australian Conference on Combinatorial Mathematics, edited by Wallis, J. and Wallis, W., T.U.N.R.A., 145–161, Newcastle, N.S.W., 1972).Google Scholar
Hall, Marshall Jr (1959), Theory of Groups, (MacMillan, New York, 1959).Google Scholar
Sprott, D. A. (1956), ‘Some series of balanced incomplete block designs’, Sankhya Ser. A 17, 185–192.Google Scholar
Storer, J. (1967), Cyclotomy and Difference Sets, (Lecturer in Advanced Mathematics, 2, Markham, Chicago, Illinois, 1967).Google Scholar
Wallis, Jennifer (1972), ‘On supplementary difference sets’, Aequations Mathematicae, 8, 242–257.CrossRefGoogle Scholar
Wallis, W. D., Street, Anne Penfold, Wallis, Jennifer Seberry (1972), Combinatorics: Room Squares, Sum-free Sets, Hadamard Matrices, (Lecture Notes in Mathematics, Vol. 292, Springer-Verlag, Berlin-Heidelberg-New York, 1972).CrossRefGoogle Scholar