On equivalence of Hadamard matrices and projection properties

The classification of Hadamard matrices of orders n greater than or equal to 32 is still remains an open and difficult problem. The definition of equivalent Hadamard matrices gets to have huge complexity as n is getting bigger. One efficient criterion (K-boxes) used for the construction of inequivalent Hadamard matrices in order 28. In this paper we use inequivalent projections of Hadamard matrices and their symmetric Hamming distances to check inequivalent Hadamard matrices. Using this criterion we developed two algorithms. The first one achieves to find all inequivalent projections in k columns as well as to classify Hadamard matrices and the second, which is faster than the first, uses the sym, metric Hamming distance distribution of projections to classify Hadamard matrices. As an example, we apply the second algorithm to the known inequivalent Hadamard matrices of orders n = 4,8,12,16,20,24 and 28.