### 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(i_{1}, 1) - h(i_{2}, 1), h(i_{1}, 2), - h(i_{2}, 2), . . . , h(i_{1}, gλ) - h(i_{2}, gλ), for any i_{1} ≠ i_{2}. In this paper, we propose a new method of expanding a GH (g^{m} , λ_{1}) = B = [B_{ij}] over G^{m} by replacing each of its m-tuple B_{ij} with B_{ij} ⊕ GH (g, λ_{2}) where m = gλ_{2}. We may use g^{m} λ_{1} (not necessarily all distinct) GH (g, λ_{2})'s for the substitution and the resulting matrix is defined over the group of order g.

Original language | English |
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Pages (from-to) | 361-364 |

Number of pages | 4 |

Journal | Journal of Communications and Networks |

Volume | 3 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Networks and Communications