Thus there exists a regular Hadamard matrix of order 4p2.
We show that for each integer n for which there is a Hadamard matrix of order 4n and 8n2−1 is a prime number, there is a productive regular Hadamard matrix of order 16n2 8n2−1)2.
We prove there is a cocyclic Hadamard matrix of order 210+tq whenever t⩾8⌊log2(q−1)10⌋.
If there exists a conference graph on 2m−1 vertices, then there exists a regular Hadamard matrix of order 4m2.
A conference graph on 2m+3 vertices yields a regular Hadamard matrix of order 4(m+1)2.
We show that a near resolvable 2- 2k+1,k,k−1 2- 2k+1,k,k−1s if andesign if a confexists matrif of order 2k+2 does.
We also show that if the binary expansion of q contains N ones, then there is a cocyclic Hadamard matrix of order 24N−2q.
Using this pair of designs, we prove there is a cocyclic Hadamard matrix of order 2ts for any odd integer s>1 and any t⩾⌊8 log2 s⌋.
DensToolKit also evaluates the momentum space electron density on spatial grids, and the reduced density matrix of order one along lines joining two arbitrary atoms of a molecule.
If n≡1 (mod 4), we have to decide if we should add a run in a n×p submatrix of a Hadamard matrix of order n, say Hn or, alternatively, if we should delete three runs from a (n+4)×p submatrix of a Hadamard matrix of order n+4, say Hn+4, in an optimal manner, respectively.
We present a new method for approximating the partition function of 2D Ising models using a transfer matrix of order 2n.
