A note on the construction of GH(4tq, EA(q)) for t=1, 2
نویسندگان
چکیده
Let GH(n; G) denote a generalised Hadamard matrix of order n over the group G, and let EA( q) denote the elementary abelian group of prime power order q. We use a computer to investigate the applicability of a recently discovered general construction for GH (4tq; E A( q)) in the case t = 2. In particular, we prove that G H (8p; Zp) exist for all primes p > 19, and obtain GH(8q; EA(q)) for all prime powers q between 19 and 200 except 27. Vve also obtain a result on the number of "solutions" of a specific form, which suggests there are many inequivalent G H (4q; E A( q)). A consequence of our argument is a recasting of the Hadamard conjecture in terms of the behaviour of the discrete Fourier transform.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 6 شماره
صفحات -
تاریخ انتشار 1992