Question

Two parties are privately communicating information given by vectors. The method of encoding the information is a linear transformation given by an commonly held m × n matrix A. Party 1 sends the message x and Party 2 receives y = Ax. If m > n could the matrix A be chosen so that Party 2 can reliably reconstruct x from y? What about m = n? What about m < n?

Two parties are privately communicating information given by vectors. The method of encoding the information is a linear transformation given by an commonly held m x n matrix A. Party 1 sends the message x and Party 2 receives y - Ax. If m > n could the matrix A be chosen so that Party 2 can reliably reconstruct x from y? What about m n? What about m < n?

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