Constructions of Relative Difference Sets with Classical Parameters and Circulant Weighing Matrices
نویسندگان
چکیده
منابع مشابه
Constructions of Relative Difference Sets with Classical Parameters and Circulant Weighing Matrices
In this paper, a new family of relative difference sets with parameters (m, n, k, λ) = ((q − 1)/(q − 1), 4(q− 1), q, q/4) is constructed where q is a 2-power. The construction is based on the technique used in [2]. By a similar method, we also construct some new circulant weighing matrices of order q where q is a 2-power, d is odd and d ≥ 5. Correspondence: S.L. Ma Department of Mathematics Nat...
متن کاملOn 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...
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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 کاملTwo Generalized Constructions of Relative Difference Sets
We give two generalizations of some known constructions of relative difference sets. The first one is a generalization of a construction of RDS by Chen, Ray-Chaudhuri and Xiang using the Galois ring GR(4,m). The second one generalizes a construction of RDS by Ma and Schmidt from the setting of chain rings to a setting of more general rings.
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2002
ISSN: 0097-3165
DOI: 10.1006/jcta.2002.3262