Over an additive abelian group G of order g and for a given positive integer λ, a generalized Hadamard matrix GH (g, λ) is defined as a gλ x gλ matrix [h(i, j)], where 1 ≤ i ≤ gλ and 1 ≤ j ≤ gλ, such that every element of G appears exactly λ times in the list h(i1, 1) - h(i2, 1), h(i1, 2), - h(i2, 2), . . . , h(i1, gλ) - h(i2, gλ), for any i1 ≠ i2. In this paper, we propose a new method of expanding a GH (gm , λ1) = B = [Bij] over Gm by replacing each of its m-tuple Bij with Bij ⊕ GH (g, λ2) where m = gλ2. We may use gm λ1 (not necessarily all distinct) GH (g, λ2)'s for the substitution and the resulting matrix is defined over the group of order g.
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Networks and Communications