Applying Balanced Generalized Weighing Matrices to Construct Block Designs

Applying Balanced Generalized Weighing Matrices to Construct Block Designs

Balanced generalized weighing matrices are applied for constructing a family of symmetric designs with parameters (1 + qr(rm+1 − 1)/(r − 1), rm, rm−1(r − 1)/q), where m is any positive integer and q and r = (qd − 1)/(q − 1) are prime powers, and a family of non-embeddable quasi-residual 2−((r+1)(rm+1−1)/(r−1), rm(r+ 1)/2, rm(r− 1)/2) designs, where m is any positive integer and r = 2d− 1, 3 · 2...

Balanced Generalized Weighing Matrices and their Applications

Balanced generalized weighing matrices include well-known classical combinatorial objects such as Hadamard matrices and conference matrices; moreover, particular classes of BGW -matrices are equivalent to certain relative difference sets. BGW -matrices admit an interesting geometrical interpretation, and in this context they generalize notions like projective planes admitting a full elation or ...

Generalized Balanced Tournament Designs with Block Size Four

In this paper, we remove the outstanding values m for which the existence of a GBTD(4,m) has not been decided previously. This leads to a complete solution to the existence problem regarding GBTD(4,m)s.

New orthogonal designs from weighing matrices

In this paper we show the existence of new orthogonal designs, based on a number of new weighing matrices of order 2n and weights 2n − 5 and 2n−9 constructed from two circulants. These new weighing matrices were constructed recently by establishing various patterns on the locations of the zeros in a potential solution, in conjunction with the power spectral density criterion. We also demonstrat...

Splitting balanced incomplete block designs