Checkered Hadamard Matrices of Order 16

In this paper all the so-called checkered Hadamard matrices of order 16 are determined (i.e., Hadamard matrices consisting of 16 square blocksHijof order 4 such thatHii = J4andHijJ4 = J4Hij = 0 fori≠jand whereJ4is the all-one matrix of order 4). It is shown that the checkered Hadamard matrices of order 16 all belong to one of the Hallʹs classes I, II or III. Moreover the so-called block equivalency classes are determined.