nonexistence of two circulant weighing matrices of weight 81

On circulant and two-circulant weighing matrices

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer ”YES”, by constructing a circulant weighing matrix of orde...

On circulant weighing matrices

Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 8 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.

Finiteness of circulant weighing matrices of fixed weight

Let n be any fixed positive integer. Every circulant weighing matrix of weight n arises from what we call an irreducible orthogonal family of weight n. We show that the number of irreducible orthogonal families of weight n is finite and thus obtain a finite algorithm for classifying all circulant weighing matrices of weight n. We also show that, for every odd prime power q, there are at most fi...

Proper Circulant Weighing Matrices of Weight 25 Ka Hin

New weighing matrices constructed from two circulant submatrices

A number of new weighing matrices constructed from two circulants and via a direct sum construction are presented, thus resolving several open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.

Some New Results on Circulant Weighing Matrices

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...