On the asymptotic existence of partial complex Hadamard matrices and related combinatorial objects

@article{Launey2000OnTA,
title={On the asymptotic existence of partial complex Hadamard matrices and related combinatorial objects},
author={Warwick de Launey},
journal={Discrete Applied Mathematics},
year={2000},
volume={102},
pages={37-45}
}

A proof of an asymptotic form of the original Goldbach conjecture for odd integers was published in 1937. In 1990, a theorem re ning that result was published. In this paper, we describe some implications of that theorem in combinatorial design theory. In particular, we show that the existence of Paley’s conference matrices implies that for any su ciently large integer k there is (at least) about one third of a complex Hadamard matrix of order 2k. This implies that, for any ¿ 0, the well known… CONTINUE READING

Although using this result would sacri ce some precision, it is really all that is needed to obtain results with the main features of those given in this paper, and there is the advantage that the ideas needed to understand the proof of Proposition 1.2 can be found in one well written book.