Design theory
A survey on relative difference sets
GDSTM '93 Proceedings of a special research quarter on Groups, difference sets, and the monster
On Relative Difference Sets in Dihedral Groups
Designs, Codes and Cryptography
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Modified generalized Hadamard matrices and constructions for transversal designs
Designs, Codes and Cryptography
A family of non class-regular symmetric transversal designs of spread type
Designs, Codes and Cryptography
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Let G be a group of order mu and U a normal subgroup of G of order u. Let G/U = {U 1,U 2, . . . ,U m } be the set of cosets of U in G. We say a matrix H = [h ij ] of order k with entries from G is a quasi-generalized Hadamard matrix with respect to the cosets G/U if $${\sum_{1\le t \le k} h_{it}h_{jt}^{-1} = \lambda_{ij1}U_1+\cdots+\lambda_{ijm}U_m (\exists\lambda_{ij1},\ldots, \exists \lambda_{ijm} \in \mathbb{Z})}$$ for any i 驴 j. On the other hand, in our previous article we defined a modified generalized Hadamard matrix GH(s, u, 驴) over a group G, from which a TD 驴 (u驴, u) admitting G as a semiregular automorphism group is obtained. In this article, we present a method for combining quasi-generalized Hadamard matrices and semiregular relative difference sets to produce modified generalized Hadamard matrices.