CHM scripts

Set of scripts supporting the catalogue of complex Hadamard matrices. Scripts were prepared and tested in:

9.1.0.441655 (R2016b) % Matlab
7.2.0 % Octave

Matlab scripts should also be runnable in Octave environment.

nomenclature (Matlab)

Script names follow the convention proposed in the catalogue. However they are slightly simplified. In particular:

• matrix name format is YN or YNX where
  • Y = symbol denoting the matrix (usually it is the first letter of the name of the author/finder)
  • N = size of the matrix
  • X = additional letter to distinguish between two or more matrices of given size
• if matrix admits a family stemming from it, the appropriate vector (matrix) of parameters (free phases) is usually denoted by R
  • for affine families a vector of free phases can be passed as a parameter; in every case free phases are normalized to unit interval: [0, 2π) → [0, 1)
  • for non-affine families it might happen that a special restriction for free phases should be imposed, e.g. M6.m

usage (Matlab)

>> H = F6(rand(1, 2))  % six-dim. Fourier with random phases
>> H = F6([rand rand]) % equivalent call
>> H = F6([0.5 0])     % custom phases

>> H = Q11X(1)         % one of four possible solutions for Q11 matrix

Mathematica users can easily adapt Matlab scrips using a copy/paste procedure...