Hamming Ball Volume

Problem

Return the number of binary words of length n within Hamming distance t of a fixed word, which is the sum of C(n, k) for k from 0 to t. Values of t above n are clamped to n. Return the count as an integer, and return 0 when t is negative.

Hint

A word at distance k differs in exactly C(n, k) patterns.

Test cases

case 1

in: [7,1]

expected: 8

case 2

in: [7,0]

expected: 1

case 3

in: [5,5]

expected: 32

case 4

in: [3,2]

expected: 7

case 5

in: [10,2]

expected: 56

Starter codePython

import math
def hamming_ball_volume(n, t):
    # Your code here
    pass

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