Expanding generalized Hadamard matrices over Gm by substituting several generalized Hadamard matrices over G

Jong Seon No, Hong Yeop Song

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)361-364
Number of pages4
JournalJournal of Communications and Networks
Volume3
Issue number4
DOIs
Publication statusPublished - 2001 Dec

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Networks and Communications

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