The Z2s -additive codes are subgroups of Z n 2s , and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s additive code. It is known that the dimension of the kernel can be used to give a complete classification of the Z4-linear Hadamard codes. In this paper, the kernel of Z2s -linear Hadamard...

It was shown by LeCompte, Martin, and Owens in 2010 that the existence of mutually unbiased Hadamard matrices and the identity matrix, which coincide with mutually unbiased bases, is equivalent to that of a Q-polynomial association scheme of class four which is both Q-antipodal and Q-bipartite. We prove that the existence of a set of mutually unbiased Bush-type Hadamard matrices is equivalent t...

The primary goal of this paper is to furnish an alternative description for the contingent normal cone, similar to the one that exists for the Fréchet one, but by using a directional convergence in place of the usual one. In fact, we actually prove that the same description is available not only for the contingent normal cone, but also for the Dini-Hadamard normal cone and the Dini-Hadamard-lik...

we present a novel technique of calibrating the interaction matrix for high-order adaptive optics systems, called the multichannel-Hadamard method. In this method, the deformable mirror actuators are firstly divided into a series of channels according to their coupling relationship, and then the voltage-oriented Hadamard method is applied to these channels. Taking the 595-element adaptive optic...

Apart from the ordinary and the periodic Golay pairs, we define also the negaperiodic Golay pairs. (They occurred first, under a different name, in a paper of Ito.) If a Hadamard matrix is also a Toeplitz matrix, we show that it must be either cyclic or negacyclic. We investigate the construction of Hadamard (and weighing matrices) from two negacyclic blocks (2N-type). The Hadamard matrices of ...

The two dimensional analog of the Hadamard state condition is used to specify the local Hadamard states associated with a linear quantum field coupled to a two dimensional gravitational background. To characterize a local Hadamard state corresponding to a physical vacuum state, we apply a superselection rule in which the state dependent part of the two-point function is determined in terms of a...

The Khatri-Rao and Tracy-Singh products for partitioned matrices are viewed as generalized Hadamard and generalized Kronecker products, respectively. We define the KhatriRao and Tracy-Singh sums for partitioned matrices as generalized Hadamard and generalized Kronecker sums and derive some results including matrix equalities and inequalities involving the two sums. Based on the connection betwe...

Bent functions f : F2 → F2 achieve largest distance to all linear functions. Equivalently, their spectrum with respect to the Hadamard-Walsh transform is flat (i.e. all spectral values have the same absolute value). That is equivalent to saying that the function f has optimum periodic autocorrelation properties. Negaperiodic correlation properties of f are related to another unitary transform c...

Let M be a Hadamard manifold, that is, a complete simply connected riemannian manifold with non-positive sectional curvatures. Then every geodesic segment α : [0, a] → M from α(0) to α(a) can be extended to a geodesic ray α : [0,∞) → M . We say then that the Hadamard manifold M is geodesically complete. Note that, in this case, all geodesic rays are proper maps. CAT(0) spaces are generalization...

In modern communication technologies, the demand of image data compression increasing rapidly. This paper presents different methods for image compression like DCT, Walsh, Hadamard and Walsh Hadamard. Main objective of this paper is to achieve the higher compression ratio and lower the Mean square error. Different test images over different orthogonal transform are used to achieve the performan...