An algorithm for orthogonal designs

Authors

Peter Eades
Peter J. Robinson
Jennifer Seberry, University of WollongongFollow
Ian S. Williams

Publication Details

Peter Eades, Peter J. Robinson, Jennifer Seberry Wallis and Ian S. Williams, An algorithm for orthogonal designs, Proceedings of the Fifth Manitoba Conference on Numerical Mathematics, Congressus Numerantium, 15, (1975), 279-292.

Abstract

Let A =(s_i) be an n-tuple of positive integers such that Es_i = 2^k. We give an algorithm which shows that there exists a p = (R_A(n, k) - (k+1)) such that there is an orthogonal design of type (2^ps₁, 2^ps₂,..., 2^ps_n) in order 2^k+p. We evaluate the maximum of p over n-tuples A which add to 2^k. Hence we deduce that for any n and k there is an integer q = max R_A(n, k) - (k+1) such that for any n-tuple A there is an orthogonal design of type 2^qA in order 2^q+k.