GBRD's: Some new constructions for difference matrices,generalised hadamard matrices and balanced generalised weighing matrices |
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Authors: | Warwick de Launey |
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Affiliation: | (1) Siromath, Pty, Ltd., CSIRO PMB 44, 0821 Winnellie, NT, Australia |
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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. |
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