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SOME INVARIANT PROPERTIES OF THE REAL HADAMARD MATRIX*
, 1974
"... Applications of wellknown matrix theory reveal some interesting and possibly useful invariant properties of the real Hadamard matrix and transform (including the Walsh matrix and transform). Subject to certain conditions that can be fulfilled for many orders of the matrix, the space it defines can ..."
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Applications of wellknown matrix theory reveal some interesting and possibly useful invariant properties of the real Hadamard matrix and transform (including the Walsh matrix and transform). Subject to certain conditions that can be fulfilled for many orders of the matrix, the space it defines can
A Hadamard matrix of order 428
"... Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T sequences. The first order of many new Hadamard matrices constructible using these new T sequences is ..."
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Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T sequences. The first order of many new Hadamard matrices constructible using these new T sequences
Positivity preserving Hadamard matrix functions
"... For every positive real number p that lies between even integers 2(m − 1) and 2m we demonstrate a matrix A = [aij] of order 2(m+1) such that A is positive definite but the matrix with entries aij p is not. 1 ..."
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For every positive real number p that lies between even integers 2(m − 1) and 2m we demonstrate a matrix A = [aij] of order 2(m+1) such that A is positive definite but the matrix with entries aij p is not. 1
A Counterexample to a Hadamard Matrix Pivot Conjecture
, 1998
"... In the study of the growth factor of completely pivoted Hadamard matrices, it becomes natural to study the possible pivots. Very little is known or provable about these pivots other than a few cases at the beginning and end. For example it is known that the first four pivots must be 1; 2; 2 and 4 an ..."
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matrix whose n \Gamma 3rd pivot is n=2 showing that the conjecture is false. Problems involving Hadamard matrices sound very easy, but they are notoriously difficult to solve. One interesting open problem that has captured the attention of a number of mathematicians is the question of the largest growth
Regular Hadamard matrix, maximum excess and SBIBD
"... When k = q1, q2, q1q2, q1q4, q2q3N, q3q4N, whereq1, q2 and q3 are prime powers, and where q1 ≡ 1(mod4),q2 ≡ 3(mod8),q3 ≡ 5(mod8),q4 =7 or 23, N =2 a 3 b t 2, a, b = 0 or 1, t = 0 is an arbitrary integer, we prove that there exist regular Hadamard matrices of order 4k 2, and also there exist SBIBD(4 ..."
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When k = q1, q2, q1q2, q1q4, q2q3N, q3q4N, whereq1, q2 and q3 are prime powers, and where q1 ≡ 1(mod4),q2 ≡ 3(mod8),q3 ≡ 5(mod8),q4 =7 or 23, N =2 a 3 b t 2, a, b = 0 or 1, t = 0 is an arbitrary integer, we prove that there exist regular Hadamard matrices of order 4k 2, and also there exist SBIBD
Bases of Cocycle Lattices and Submatrices of a Hadamard Matrix
, 1998
"... We study the lattice lat(M) of cocycles of a binary matroid M . By an isomorphism we show that such lattices are equivalent to lattices generated by the columns of proper submatrices of Sylvester matrices of full row length. As an application we show that the cocycle lattice of a recursively defined ..."
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We study the lattice lat(M) of cocycles of a binary matroid M . By an isomorphism we show that such lattices are equivalent to lattices generated by the columns of proper submatrices of Sylvester matrices of full row length. As an application we show that the cocycle lattice of a recursively defined class of matroids, including all binary matroids of rank four, always has a basis consisting of cocycles.
On the Least Number of Cell Orbits of a Hadamard Matrix of Order n
"... Abstract. The automorphism group of any Hadamard matrix of order n acts on the set of cell coordinates {(i, j)  i, j = 1, 2,..., n}. Let f(n) denote the least number of cell orbits amongst all the Hadamard matrices of order n. This paper describes Hadamard matrices with a small number of cellwis ..."
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Abstract. The automorphism group of any Hadamard matrix of order n acts on the set of cell coordinates {(i, j)  i, j = 1, 2,..., n}. Let f(n) denote the least number of cell orbits amongst all the Hadamard matrices of order n. This paper describes Hadamard matrices with a small number
The Impact of Number Theory and Computer Aided Mathematics on Solving the Hadamard Matrix Conjecture
"... In memory of Alf van der Poorten The Hadamard Conjecture has been studied since the pioneering paper of J. J. Sylvester, “Thoughts on inverse orthogonal matrices, simultaneous sign successions, tessellated pavements in two or more colours, with applications to Newtons rule, ornamental tile work and ..."
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In memory of Alf van der Poorten The Hadamard Conjecture has been studied since the pioneering paper of J. J. Sylvester, “Thoughts on inverse orthogonal matrices, simultaneous sign successions, tessellated pavements in two or more colours, with applications to Newtons rule, ornamental tile work
design⇐ ⇒ ∃ Hadamard matrix Hn. • A Hadamard matrix Hn of order n is an n×n matrix of +1’s and −1’s such that
, 2008
"... In this talk, we give a simple method for computing the stabilizer subgroup of the set of solutions of certain algebraic curves in projective general linear group over finite fields. Using this we construct new infinite families of 3designs. ..."
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In this talk, we give a simple method for computing the stabilizer subgroup of the set of solutions of certain algebraic curves in projective general linear group over finite fields. Using this we construct new infinite families of 3designs.
A Method for Privacy Preserving Data Mining in Secure Multiparty Computation using Hadamard Matrix
"... Abstract Secure multiparty computation allows multiple parties to participate in a computation. SMC (secure multiparty computation) assumes n parties where n>1. All the parties jointly compute a function. Privacy preserving data mining has become an emerging field in the secure multiparty comput ..."
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computation. Privacy preserving data mining preserves the privacy of individual's data. Privacy preserving data mining outputs have the property that the only information learned by the different parties is only the output of the algorithm. In this paper, we use a mathematical function hadamard matrix
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