author={Jean-Marie Goethals and J. J. Seidel},
  journal={Canadian Journal of Mathematics},
1. Introduction. C-matrices appear in the literature at various places; for a survey, see [11]. Important for the construction of Hadamard matrices are the symmetric C-matrices, of order v = 2 (mod 4), and the skew C-matrices, of order v = 0 (mod 4). In § 2 of the present paper it is shown that there are essentially no other C-matrices. A more general class of matrices with zero diagonal is investigated, which contains the C-matrices and the matrices of (v, k, X)-systems on k and k + 1 in the… Expand
Non-skew symmetric orthogonal matrices with constant diagonals
  • C. Lam
  • Computer Science, Mathematics
  • Discret. Math.
  • 1983
This paper restricts the study to orthogonal matrices with a constant m > 1 on the diagonal and +/-1's off the diagonal, and it is shown that if m is even and n=0 (mod 4), then an Orthogonal matrix must be skew symmetric. Expand
Some matrices of Williamson type
Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and four (1,-1) matrices A, B, C, D of order m which are of Williamson type; that is,Expand
Some classes of Hadamard matrices with constant diagonal
The concepts of circulant and back circulant matrices are generalized to obtain incidence matrices of subsets of finite additive abelian groups. These results are then used to show the existence ofExpand
Eigenvalues of a class of (0,±1) symmetric matrices
Abstract Let G ( n ) denote the class of all symmetric matrices of order n with zero diagonal and off-diagonal entries ±1. For any C ϵ G ( n ), let f ( C ) denote a maximum eigenvalue of C 2 , andExpand
J ul 2 01 9 A new family of Hadamard matrices of order 4 ( 2 q 2 + 1 )
A Hadamard matrix of order v is a v×v matrixH with entries ±1 such thatHH = vI, where I is the identity matrix. It can be easily shown that if H is a Hadamard matrix of order v, then v = 1, 2, or 4tExpand
Some (1, -1) Matrices
Abstract We define an n -type (1, −1) matrix N = I + R of order n ≡ 2 (mod 4) to have R symmetric and R 2 = ( n − 1) I n . These matrices are analogous to skew-type matrices M = I + W which have WExpand
Conference Matrices from Projective Planes of Order 9
The tools are considerations of symmetry, use of a computer, and general results such as the following, which show that these constructions reduce to 26 nonequivalent conference matrices of order 82, which give rise to 175 nonisomorphic strongly regular graphs. Expand
Gröbner bases and cocyclic Hadamard matrices
An alternative polynomial ideal that also characterizes the set of cocyclic Hadamard matrices over a fixed finite group G of order 4t is described and the complexity of the computation decreases to 2 O ( t ) . Expand
Generalized conference matrices and projective planes
This work will obtain a short proof of the following result: if a finite projective plane of even order is (a,A)- and (b,B)-transitive with B=ab and b=AB and if the group of all (a-A)-homologies is abelian, then the groupof all (b-B)-elations is elementary abelians and therefore the order of the plane is a power of 2. Expand
Abstract : The incidence matrix A of a (v,k,lambda)-design satisfies A(A superscript T) + (k - lambda)I + lambda J, where (A superscript T) denotes the transpose of A. The matrix I is the identityExpand


Note on Hadamard's determinant theorem
Introduction. We shall call a square matrix A of order n an Hadamard matrix or for brevity an iî-matrix, if each element of A has the value ± 1 and if the determinant of A has the maximum possibleExpand
Strongly Regular Graphs of L2-type and of Triangular Type
This chapter discusses strongly regular graphs of L 2 -type and of triangular type. The theory of strongly regular graphs includes the theory of orthogonal latin squares. In a number of cases, it isExpand
Equilateral point sets in elliptic geometry
This chapter highlights equilateral point sets in elliptic geometry. Elliptic space of r−1 dimensions E r−1 is obtained from r -dimensional vector space R r with inner product ( a , b ). For 1 , anyExpand
Strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3
The ordinary graphs of finite order ν with (−1, 1, 0) adjacency matrix A satisfying ( A − ρ 1 I ) ( A − ρ 2 I ) = (ν − 1 + ρ 1 ρ 2 ) J , ρ 1 ρ 2 , AJ= ρ 0 J . The only eigenvalues are ρ 1 , ρ 2 , ρ 0Expand
Relations Among Generalized Hadamard Matrices, Relative Difference Sets, and Maximal Length Linear Recurring Sequences
It was established in (5) that the existence of a Hadamard matrix of order 4 t is equivalent to the existence of a symmetrical balanced incomplete block design with parameters v = 4 t — 1, k = 2 t —Expand
Finite permutation groups of rank 3
By the rank of a transitive permutation group we mean the number of orbits of the stabilizer of a point thus rank 2 means multiple transitivity. Interest is drawn to the simply transitive groups ofExpand
Strongly regular graphs, partial geometries and partially balanced designs.
This paper introduced the concept of a partial geometry, which serves to unify and generalize certain theorems on embedding of nets, and uniqueness of association schemes of partially balancedExpand
A Note on the Parameters of PBIB Association Schemes
This paper presents several results on association scheme parameters of partially balanced designs, dealing mostly with divisibility properties and based on the standard identities relating theseExpand
Some Aspects of Weighing Designs
Relative difference sets