How to efficiently create generator Matrix using Reed-Solomon encoding

Question

I am coding a function to create generator matrix using Reed-Solomon encoding in Python. it is currently using for loops but i was wondering if there is a more efficient way to this. My code is:

def ReedSolomon(k,p):
    M = np.zeros((k,p))
    for i in range(k):
        for j in range(p):
            M[i][j] = j**i 
    return M

The encoding is:

I believe my function works but may not scale well to large p and k

Answer 1

The generalized equation for an element at index r, c in your matrix is c**r.

For a matrix of shape k, p, you can create two aranges -- a row vector from 0 to p-1, and a column vector from 0 to k-1, and have numpy automatically broadcast the shapes:

def ReedSolomon(k,p):
    rr = np.arange(k).reshape((-1, 1))
    cc = np.arange(p)
    return cc**rr

Calling this function with e.g. k=5, p=3 gives:

>>> ReedSolomon(5, 3)
array([[ 1,  1,  1],
       [ 0,  1,  2],
       [ 0,  1,  4],
       [ 0,  1,  8],
       [ 0,  1, 16]])