1. The concept is a generalization of the Hadamard matrix . 2. If a Hadamard matrix is normalized and fractionated, a design pattern is obtained. 3. Unfortunately, there may not be a Hadamard matrix of size " s ". 4. As a result, the smallest order for which no Hadamard matrix is presently known is 668. 5. Similar techniques can be applied for multiplications by matrices such as Hadamard matrix and the Walsh matrix. 6. The size of a Hadamard matrix must be 1, 2, or a multiple of 4. 7. This implementation follows the recursive definition of the 2N \ times 2N Hadamard matrix H _ N: 8. A Hadamard matrix of this order was found using a computer by Williamson, that has yielded many additional orders. 9. In 2005, Hadi Kharaghani and Behruz Tayfeh-Rezaie published their construction of a Hadamard matrix of order 428. 10. Thus, \ mathit { x K } is the standard form of some complex Hadamard matrix \ mathit { H }.