ABSTRACT
This chapter explains how to construct new Hadamard matrices with maximal excess and infinitely many new symmetric balanced incomplete block design (SBIBD). It presents introduction to the new Hadamard matrices of order n. A regular Hadamard matrix has constant row and column sum. These are discussed by Seberry Wallis. A SBIBD is defined as a square matrix of order v with entries 0 or 1. Suitable matrices are matrices with elements +1 and -1 which can be used to replace the variables of orthogonal design (OD) to form Hadamard matrices. The practice for constructing Hadamard matrices derived from extensions due to Baumert-Hall who found the first OD and J. Cooper and J. (Seberry) Wallis who first introduced T-matrices to form OD.
