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International Conference on Statistics, Combinatorics and Related Areas - 7th International Conference of the Forum for Interdisciplinary Mathematics
December 19-21, 2000
Indian Institute of Technology-Bombay
Mumbai, Maharastra, India

Organizers
Satya N. Mishra (University of South Alabama), Sanjeev V. Sabnis (IIT, Bombay)

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Construction of some A-optimal weighing design when n = 3 (mod 4)
by
R. G. Shenoy
Department of Statistics,University of Mumbai,Mumbai-400098, India

Let n and N be two positive integers with n <= N. X(N, n) denote the set of all N ×n matrices X with xij = +1 or -1. Such a matrix is called weighing matrix. If X* minimises trace(X'X)inverse over X(N, n) then X* is said to be A-optimal weighing design. For N=3(mod4), a lower bound for tr(X'X)inverse has been obtained and it is shown that this bound is attained if X is such that X'X is block matrix with specified blocks of only one size or of two contiguous sizes.In this paper some A-Optimal X attianing the lower bound for n <= N-3 are constructed by deleting s-4 specified rows of a Hadamard matrix of order N-3 and then augmenting it by Specified rows for s= 5, 6, 7, 8.

Date received: November 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafx-18.