Generalised Hadamard matrices which are developed modulo a group

17Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.

Abstract

Let N and G be finite groups with orders n and g, respectively, and let q be a prime power. Also, let EA(q) be the elementary abelian group of order q, and let EA(n) be the group of order n which is the direct product of elementary abelian groups. This paper discusses generalised Hadamard matrices, GH(n; G), which are developed modulo a group N. These matrices have been called N-invariant GH-matrices and they are equivalent to G-relative difference sets, RDS(g, n, n, 0, n/g), modulo the direct sum of N and G. Contained in this paper are simple constructions for GH(q; EA(q)), q odd, developed modulo EA(q), and GH(q2; G), developed modulo EA(q2). Also, an algebraic setting for the study of these designs is developed, and non-existence results are obtained. Indeed, in all but 15 of the 108 cases with n≤50, the existence of a GH(n; EA(q)), developed modulo EA(n), is either proved or disproved. In addition, a result on the non-existence of generalised weighing matrices developed modulo a group is presented. Finally a connection with error-correcting codes is presented, and it is proved that if n≥g(g-1) then every element of G must appear in any GH(n; G) developed modulo a group. © 1992.

Cite

CITATION STYLE

APA

de Launey, W. (1992). Generalised Hadamard matrices which are developed modulo a group. Discrete Mathematics, 104(1), 49–65. https://doi.org/10.1016/0012-365X(92)90624-O

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free