Hamming Bound Check

Problem

Check the sphere-packing (Hamming) bound for a binary code with parameters (n, k, d). With t = floor((d - 1) / 2), return True when the number of words in a radius-t sphere around a codeword, sum_{i=0}^{t} C(n, i), does not exceed the number of syndromes 2^(n - k).

Hint

Perfect codes such as Hamming(7,4) meet the bound with equality.

Test cases

case 1

in: [7,4,3]

expected: true

case 2

in: [4,2,3]

expected: false

case 3

in: [3,1,3]

expected: true

case 4

in: [7,3,4]

expected: true

case 5

in: [5,2,3]

expected: true

Starter codePython

import math
def hamming_bound_holds(n, k, d):
    # Your code here
    pass

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