Regularity questions for complex Hadamard matrices

Abstract

We study the partial Hadamard matrices $H\in M_{M\times N}(\mathbb{C})$ which are regular, in the sense that the scalar products between pairs of distinct rows decompose as sums of cycles (rotated sums of roots of unity). The simplest non-trivial case is M=3, and we obtain here several results, notably with a classification at N=7. We discuss as well the potential applications of the M=3 results to various $M=N$ questions.

Withdrawn by the authors - the main findings in this paper are now part of arXiv:1706.00986

References in corpus (1)

• First order deformations of the Fourier matrix