Graphs and Combinatorics

, Volume 5, Issue 1, pp 125–135 | Cite as

GBRD's: Some new constructions for difference matrices, generalised hadamard matrices and balanced generalised weighing matrices

  • Warwick de Launey
Article

Abstract

A new construction is given for difference matrices. The generalized Hadamard matrices GH(q(q − 1)2; EA(q)) are constructed whenq andq − 1 are both prime powers. Other generalised Hadamard matrices are also shown to exist. For example, there exist GH(n; G) forn = 52 ⋅ 2 ⋅ 3, 26 ⋅ 32, 112 ⋅ 22 ⋅ 3, 172 ⋅ 2 ⋅ 32, 532 ⋅ 2 ⋅ 33, 712 ⋅ 22 ⋅ 32, 1072 ⋅ 22 ⋅ 33, 1492 ⋅ 52 ⋅ 2 ⋅ 3,.... Finally, a new construction for the BGW ((q4 − 1)/(q − 1),q3,q2(q − 1);qq-1), and a construction for the new BGW ((q8 − 1)/(q2 − 1),q6,q4(q2 − 1);G) are given, wheneverq is a prime power, andG is a group of orderq + 1.

Keywords

Prime Power Hadamard Matrice Difference Matrice Generalise Hadamard Matrice 

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Warwick de Launey
    • 1
  1. 1.Siromath, Pty, Ltd.WinnellieAustralia

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