difference set, Hadamard A (u,k,A) difference set is a k-element subset D of a group G of order u for which the multiset {dldl2: dl,d2 E D, dl =t= d2} contains each nonidentity element of G exactly A times. A Hadamard difference set (HDS) has parameters of the form (u,k, A) = (4N2,2N2_N, N2·N). The Hadamard parameters provide the richest source of known examples of difference sets. The central ...

Hadamard transform spatial multiplexing techniques are applied to laser densitometry in order to prevent the photo-induced degradation of sensitive materials. Photochemical and thermal degradations can often occur in point focused scanning laser densitometry. In spatial multiplexing, the excitation source is defocused and efficiently distributed throughout the sample, reducing local power densi...

Random and natural textures classification is still one of the biggest challenges in the field of image processing and pattern recognition. In this paper, texture feature extraction using Slant Hadamard Transform was studied and compared to other signal processing-based texture classification schemes. A parametric SHT was also introduced and employed for natural textures feature extraction. We ...

In our previous work, we introduced the following relaxation of the Hadamard property: a square matrix H ∈ MN (R) is called “almost Hadamard” if U = H/ √ N is orthogonal, and locally maximizes the 1-norm on O(N). We review our previous results, notably with the formulation of a new question, regarding the circulant and symmetric case. We discuss then an extension of the almost Hadamard matrix f...

The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex (6 × 6) Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computati...

Under the entrywise dominance partial ordering, T.L. Markham and R.L. Smith obtained a Schur complement inequality for the Hadamard product of two tridiagonal totally nonnegative matrices. Applying the properties of the Hadamard core of totally nonnegative matrices, the Schur complement inequalities for the Hadamard product of totally nonnegative matrices is obtained, which extends those of T.L...

Hadamard multiplexing provides a considerable SNR boost over additive random noise but Poisson noise such as photon noise reduces the boost. We develop the theory for full H-matrix Hadamard transform imaging under additive and Poisson noise effects. We show that H-matrix encoding results in no effect on average on the noise level due to Poisson noise sources while preferentially reducing additi...

Under the entrywise dominance partial ordering, T.L. Markham and R.L. Smith obtained a Schur complement inequality for the Hadamard product of two tridiagonal totally nonnegative matrices. Applying the properties of the Hadamard core of totally nonnegative matrices, the Schur complement inequalities for the Hadamard product of totally nonnegative matrices is obtained, which extends those of T.L...

Using a class of permutation polynomials of F32h+1 obtained from the Ree–Tits slice symplectic spreads in PG(3,32h+1), we construct a family of skew Hadamard difference sets in the additive group of F32h+1 . With the help of a computer, we show that these skew Hadamard difference sets are new when h= 2 and h = 3. We conjecture that they are always new when h > 3. Furthermore, we present a varia...