Hamming (7,4) Payload Bits

Problem

Correct at most one bit error in a received Hamming (7,4) word and return the four data bits. Positions 1 through 7 hold p1, p2, d1, p4, d2, d3, d4; the syndrome is the XOR of the 1-based positions of the set bits, and a nonzero syndrome flips that position. Return the data bits in order d1, d2, d3, d4.

Hint

Compute the syndrome from the parity positions, fix the indicated bit, then read positions 3, 5, 6, and 7.

Test cases

case 1

in: [[0,1,1,0,0,1,1]]

expected: [1,0,1,1]

case 2

in: [[0,1,1,0,1,1,1]]

expected: [1,0,1,1]

case 3

in: [[1,1,1,1,1,1,1]]

expected: [1,1,1,1]

case 4

in: [[0,0,0,0,0,0,0]]

expected: [0,0,0,0]

case 5

in: [[0,0,1,0,0,1,1]]

expected: [1,0,1,1]

Starter codePython

def hamming74_payload(received):
    # Your code here
    pass

5 test cases · run your code against them in the editor