Balanced Weighing Matrices
Hadi Kharaghani, Thomas Pender, Sho Suda

TL;DR
This paper introduces a unified method for constructing weighing matrices and symmetric designs, especially when the weight is a prime power, and explores their connections with association schemes.
Contribution
It provides a general construction framework for weighing matrices with prime power weights and links these matrices to association schemes.
Findings
Constructed new classes of weighing matrices for prime power weights.
Established a connection between weighing matrices and association schemes.
Reduced special cases to classical balanced weighing matrices.
Abstract
A unified approach to the construction of weighing matrices and certain symmetric designs is presented. Assuming the weight in a weighing matrix is a prime power, it is shown that there is a for each positive integer . The case of reduces to the balanced weighing matrices with classical parameters The equivalence with certain classes of association schemes is discussed in details.
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Taxonomy
Topicsgraph theory and CDMA systems
