We obtain a few structural theorems for circulant weighing matrices whose weight is the square of a prime number. Our results provide new schemes to search for these objects. We also establish the existence status of several previously open cases of circulant weighing matrices. More specifically we show their nonexistence for the parameter pairs (n, k) (here n is the order of the matrix and k i...

Balanced generalized weighing matrices include well-known classical combinatorial objects such as Hadamard matrices and conference matrices; moreover, particular classes of BGW -matrices are equivalent to certain relative difference sets. BGW -matrices admit an interesting geometrical interpretation, and in this context they generalize notions like projective planes admitting a full elation or ...

Abstract. Quantum computation in the one-way model requires the preparation of certain resource states known as cluster states. We describe how the construction of continuous-variable cluster states for optical quantum computing relate to the existence of certain families of matrices. The relevant matrices are known as weighing matrices, with a few additional constraints. We prove some results ...

Divisible design digraphs are constructed from skew balanced generalized weighing matrices and Hadamard matrices. Commutative non-commutative association schemes shown to be attached the divisible digraphs.

Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying the conditions that the number of non-zero weights of the code is four and the code contains the first order Reed–Muller code. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes satisfying the conditions are determined. We also give ...

Circulant weighing matrices of order n with weight k, denoted by WC(n, k), are investigated. Under some conditions, we show that the existence of WC(n, k) implies that of WCG, ~). Our results establish the nonexistence of WC(n,k) for the pairs (n,k) = (125,25), (44,36), (64,36), (66,36), (80,36), (72,36), (118,36), (128,36), (136,36), (128,100), (144,100), (152,100), (88,36), (132,36), (160,36)...

Perfect ternary arrays are closely related to difference sets and group invariant weighing matrices. A previous paper by one of the authors demonstrated strong restrictions on difference sets with parameters (120, 35, 10). A perfect ternary array with energy 25 and order 60 – PTA(60,25) – would obey an equation analogous to the difference set equation for (120, 35, 10). A perfect ternary array ...