If possible, each element of each matrix should be a*exp(-2k*pi/2n), (k, n = positive integers, a > 0) or zero.
Well... In fact, there are some conditions: each matrix must be unitary and the elements of each matrix should be a*exp(-2k*pi/2^n), (k, n = positive integers, a > 0) or zero. I have a multiplicative group of 128 matrices verifying these conditions (for n=3). I have also the Weyl group with 192 matrices but I need more matrices. I also need to obtain the maximum value of the minimum Euclidean distance between any 2 different matrices A and B of the group. For me, the task is not obvious...
Just an idea, I think you need coding theory, cyclotomic polynomials.
I wish you can find something in this link
http://www.cse.ust.hk/faculty/cding/JOURNALS/it992.pdf
Thank you, Hanifa, for the interesting paper. In fact, I need a large group of unitary matrices for coding the input binary data for a differential, MIMO scheme. Therefore, some new elements concerning the coding theory could help.
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