Equi-angular tight frame via conference matrix 1.0

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Input parametersp : odd prime numberdeg: positive integer (default value = 1)Output is a (p^deg+1) by (p^deg+1)/2 matrix EWhen deg > 1, the communication toolbox is requiredA collection of d-dimensional vectors of norm 1 is equi-angularif the absolute values of the inner products between any twodistinct vectors is equal to a constant c.The equi-angular vectors are called tight if the constant cattains Welch's lower bound.The columns of the output matrix E is an equi-angular tight frameThe norm of each column of E is 1The inner product between each pair of columns is 1/sqrt(p^deg)Columns of E represent equi-angular linesin the (p^deg+1)/2 dimensional Euclidean spaceExample:>> 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 -0.4472We can check that diagonal entries of E'*E are all 1,and the off-diagonal entries of abs(E'*E) are all 1/sqrt(q)

Requirements: No special requirements

Platforms: Matlab

Keyword: Bound, Columns, Dimensional, Euclidean, Lines, Represent, Space, Sqrtpdeg

Users rating: 0/10

License: Shareware

Size: 10 KB

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