Input parameters
p : odd prime number
deg: positive integer (default value = 1)
Output is a (p^deg+1) by (p^deg+1)/2 matrix E
When deg > 1, the communication toolbox is required
A collection of ddimensional vectors of norm 1 is equiangular
if the absolute values of the inner products between any two
distinct vectors is equal to a constant c.
The equiangular vectors are called tight if the constant c
attains Welch's lower bound.
The columns of the output matrix E is an equiangular tight frame
The norm of each column of E is 1
The inner product between each pair of columns is 1/sqrt(p^deg)
Columns of E represent equiangular lines
in the (p^deg+1)/2 dimensional Euclidean space
Example:
>> tight_frame_paley(5)
ans =
0.0000 0.8944 0.2764 0.7236 0.7236 0.2764
0.0000 0.0000 0.8507 0.5257 0.5257 0.8507
1.0000 0.4472 0.4472 0.4472 0.4472 0.4472
We can check that diagonal entries of E'*E are all 1,
and the offdiagonal entries of abs(E'*E) are all 1/sqrt(q)
