For every n divisible by 4, we construct a square matrix H of size n, with coeecients 1, such that H H t nI mod 32. This solves the 32-modular version of the classical Hadamard conjecture. We also determine the set of lengths of 16-modular Golay sequences. 0. Introduction Hadamard matrices can be constructed from various binary sequences, either from Golay complementary sequences, or Williamson...

In [2] Bussemaker and Tonchev constructed six doubly even (56,28, 12) codes from two Hadamard matrices of order 28. But two of them were not distinguished. In [11] and [12] we characterized Hadamard matrices of order 28 and there are exactly 487 Hadamard matrices, up to equivalence. In this paper we show that only two of the above 487 matrices produce six doubly even (56,28,12) codes and that t...

Over the past couple of years trace maps over Galois fields and Galois rings have been used very successfully to construct cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and subsequently to generate simplex codes over Z4,Z2s and Zp and new linear codes over Zps . Here we define a new map, the trace-like map and more generally the weighted-trace map and extend these techniques ...

We apply Computational Algebra methods to the construction of Hadamard matrices with two circulant cores, given by Fletcher, Gysin and Seberry. We introduce the concept of Hadamard ideal for this construction to systematize the application of Computational Algebra methods. Our approach yields an exhaustive search construction of Hadamard matrices with two circulant cores for this construction f...

We consider a new operation on the family of binary relations on integers called Hadamard star. View a binary relation R ⊆ N × N as a mapping of N into the power set of N and let R(n) denote the subset of integers m such that (n,m) ∈ R. Then the Hadamard star of R is the relation which assigns to each integer n the Kleene star of R(n). This is reminiscent of the Hadamard inverse of series with ...

In this paper we did a generalization of Hadamard product of Fibonacci Q matrix and Fibonacci Q−n matrix for continuous domain. We obtained Hadamard product of the golden matrices in the terms of the symmetrical hyperbolic Fibonacci functions and investigated some properties of Hadamard product of the golden matrices. Mathematics Subject Classification: Primary 11B25, 11B37, 11B39, Secondary 11C20

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

We analyze properties of a map f sending a unitary matrix U of size N into a doubly stochastic matrix B = f (U) defined by Bi,j = |Ui,j| 2. For any U we define its defect, determined by the dimension of the image Df (TU U) of the space TU U tangent to the manifold of unitary matrices U at U under the tangent map Df corresponding to f. The defect, equal to zero for a generic unitary matrix, give...

We present in this paper the construction of a pseudodifferential calculus on smooth non-compact manifolds associated to a globally defined and coordinate independant complete symbol calculus, that generalizes the standard pseudodifferential calculus on Rn. We consider the case of manifolds M with linearization in the sense of Bokobza-Haggiag [4], such that the associated (abstract) exponential...