Skew Hadamard designs (4n−1, 2n−1, n−1) are associated to order 4n skew Hadamard matrices in the natural way. We study the codes spanned by their incidence matrices A and by I +A and show that they are self-dual after extension (resp. extension and augmentation) over fields of characteristic dividing n. Quadratic Residues codes are obtained in the case of the Paley matrix. Results on the p−rank...

Computational Algebra methods have been used successfully in various problems in many fields of Mathematics. Computational Algebra encompasses a set of powerful algorithms for studying ideals in polynomial rings and solving systems of nonlinear polynomial equations efficiently. The theory of Gröbner bases is a cornerstone of Computational Algebra, since it provides us with a constructive way of...

Automorphism groupS of Hadamard matrices are related to automorphism groups of de.Jigns, and the automorphism groups of the Paley-Hadamard matrices are determined .

If (V = j 1, • • • , n |, D CN x N, and F is an equivalence relation on the "entries" of D the reduced incidence space g(f ) is the set of all real matrices A with support in D and such that a.. = a whenrr ij rs ever (i, j)F(r, s). Let S(D) be the lattice of all subspaces of R having support contained in D, and S(D) that of all equivalences on D. Then the map g defined above is Galois connected...

A novel method to obtain parameterizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into...

In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with Hadamard product of real symmetric positive definite matrices. Since condition that a matrix A converges to zero is not needed, produces stronger results than those Perov. As an application our results, study existence and uniqueness solution for system equations.

A recently proposed matrix factorization for aHadamard matrix of order twelve is shown to be invalid in that thefactored matrix is not Hadamard.

the purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. relevant connections of the results, which are presented in the paper, with various known results are also considered.

The classical Hermite-Hadamard inequality characterizes the continuous convex functions of one real variable. The aim of the present paper is to give an analogous characterization for functions of a vector variable. 1. The Hermite-Hadamard inequality In a letter sent on November 22, 1881, to the journal Mathesis (and published there two years later), Ch. Hermite [10] noted that every convex fun...