11. Hadamard matrix is formed by rearranging the rows so that the number of sign-changes in a row is in increasing order.12. The circulant Hadamard matrix conjecture, however, asserts that, apart from the known 1? and 4? examples, no such matrices exist. 13. The Hadamard code, by contrast, is constructed from the Hadamard matrix H _ { 2 ^ n } by a slightly different procedure. 14. The number of Hadamard designs from each Hadamard matrix is 23 choose 6; that is 100, 947 designs from each 24?4 Hadamard matrix. 15. The number of Hadamard designs from each Hadamard matrix is 23 choose 6; that is 100, 947 designs from each 24?4 Hadamard matrix . 16. For the second FEC layer : every ASCII character is encoded as one of 64 possible Walsh functions ( or vectors of a Hadamard matrix ). 17. In that case, other statistical methods may be used to fractionate a Hadamard matrix in such a way that allows only a tolerable amount of aliasing. 18. This construction demonstrates that the rows of the Hadamard matrix H _ { 2 ^ n } can be viewed as a length 2 ^ n linear generating matrix F _ n. 19. Given an Hadamard matrix of size 4 " a " in standardized form, remove the first row and first column and convert every " 1 to a 0. 20. Let " H " be an Hadamard matrix of order 4 " m " in standardized form ( first row and column entries are all + 1 ).