A reduction theorem for circulant weighing matrices
نویسنده
چکیده
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), (166,36), (176,36), (198, 36), (200, 36), (200,100). All these cases were previously open.
منابع مشابه
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...
متن کاملOn 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.
متن کاملSome 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...
متن کاملFiniteness 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...
متن کاملNew 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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 18 شماره
صفحات -
تاریخ انتشار 1998