Higher SPIN alternating sign matrices.
Let be an matrix of zeros and ones. The matrix is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero -entry. We characterize all linear maps perserving the set of Ferrers vectors over the binary Boolean semiring and over the Boolean ring . Also, we have achieved the number of these linear maps in each case.
We give a construction for regular Hadamard matrices of order where is the order of a Hadamard matrix and is the order of a regular Hadamard matrix. The construction can be used to construct regular Hadamard matrices with special properties and includes several constructions which have been given previously. In the final section we consider the case in more detail.