A construction for modified generalized Hadamard matrices using QGH matrices

作者：Hiramine Yutaka^*

来源：Designs, Codes and Cryptography, 2012, 62(3): 279-288.

DOI：10.1007/s10623-011-9517-x

• Transversal design
• Generalized Hadamard matrix
• Semiregular relative difference set

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 Sigma(1 %26lt;= t %26lt;= k) h(it)h(ht)(-1) = lambda(ij1) U-1+ ... + lambda(ijm) U-m (there exists lambda(ij1), ... , there exists lambda(ijm)) for any i not equal j. On the other hand, in our previous article we defined a modified generalized Hadamard matrix GH(s, u, lambda) over a group G, from which a TD lambda(u lambda, 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.

• 出版日期2012-3