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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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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