Determination of all possible orders of weight 16 circulant weighing matrices

nonexistence of two circulant weighing matrices of weight 81

‎in this paper‎, ‎we prove the nonexistence of two weighing matrices of‎ ‎weight 81‎, ‎namely $cw(88,81)$ and $cw(99,81)$‎. ‎we will apply two‎ ‎very different methods to do so; for the case of $cw(88,81)$‎, ‎we‎  ‎will use almost purely counting methods‎, ‎while for $cw(99,81)$‎, ‎we‎ ‎will use algebraic methods‎.

The Classification of Circulant Weighing Matrices of Weight 16 and Odd Order

In this paper we completely classify the circulant weighing matrices of weight 16 and odd order. It turns out that the order must be an odd multiple of either 21 or 31. Up to equivalence, there are two distinct matrices in CW (31, 16), one matrix in CW (21, 16) and another one in CW (63, 16) (not obtainable by Kronecker product from CW (21, 16)). The classification uses a multiplier existence t...

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