By using the (generalized) Goethals-Seidel array, we construct Hadamard matrices of skew type of order 4n for n = 81,103,151,169, and 463. Hadamard matrices of skew type for these orders are constructed here for the first time. Consequently the list of odd integers n < 300 for which no Hadamard matrix of skew type of order 4n is presently known is reduced to 45 numbers (see the comments after t...

A new construction of complex Hadamard matrices of composite order d = pq, with primes p, q, is presented which is based on pairs of mutually unbiased bases containing only product states. We illustrate the method for many product dimensions d < 100 by analytically deriving complex Hadamard matrices, both with zero and non-zero defect. In particular, we obtain at least 12 new isolated Butson-ty...

In this paper, we give an algorithm to list and classify generalized Hadamard matrices of a given order over an arbitrary elementary Abelian group. Generalized Hadamard matrices of order less than or equal to 16 over Abelian groups Z3; Z4, Z2 Z2 and Z5 have been classi…ed up to equivalence. We have shown that generalized Hadamard matrices of order 4; 8, and 12 over EA(4) are unique up to equiva...

In this paper, we obtain several nonexistence results for abelian Hadamard diier-ence sets. In particular, we prove that there are no Hadamard diierence sets in abelian groups G = Z 2 Z 2 P , where jPj = p 2 , is odd and p is a prime congruent to 1(mod 4). Also we give a detailed proof for a connection between certain reversible Hadamard diierence sets and projective three-weight codes which wa...

It is shown that SBIED(4k 2 , 2Jc 2 ± k, P ± k) and Hadamard matrices with maximal excess exist for qs,q {q:q 1 (mod 4) is a prime power}, + 1, g the length of a Golay sequence}. There a proper n dimensional Hadamard matrix of order (4k2)n. Regular symmetric Hadamard matrices with constant diagonal are obtained for orders 4k2 whenever complete regular 4-sets of regular matrices of order k 2 exist.

We give an introduction to the techniques from microlocal analysis that have successfully been applied in the investigation of Hadamard states of free quantum field theories on curved spacetimes. The calculation of the wave front set of the two point function of the free Klein-Gordon field in a Hadamard state is reviewed, and the polarization set of a Hadamard two point function of the free Dir...

Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2, . . . , 16. In particular, we explicitly write down some families of complex Hadamard matrices for N = 12, 14 and 16, w...

The technique of Hadamard transform was successfully coupled with GC/nonresonant multiphoton ionization/TOFMS, for the first time. 1,4-Dichlorobenzene and the fourth harmonic generation (266 nm) of a Nd:YAG laser were employed as a model sample and an ionization laser, respectively. A Hadamard-injector coupled with a capillary-based supersonic jet nozzle (capillary-injector) was also developed ...

In [1], Constantine proposed that a variant of the codes constructed in Theorem 1 might be a useful substitute for Hadamard matrices at orders where no Hadamard matrix is known to exist. His main result is a plug-in construction for codes of order 4q with 8q codewords and minimum distance 2q−2 using a Goethals-Seidel type array. He provides component matrices for odd prime powers q. Theorem 1 s...

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.