Playing with the idea of a Hamming ball. This calculates the Hamming ball starting at a given number, with given number of bits and given radius.

hamming-ball.py

#!/usr/bin/env python3

# What is a hamming ball?
#
# I couldn't find any definition for it on the Internets. But reading between the lines
# of what people in the know say, I'll take a stab at a preliminary definition. Don't
# trust this... I haven't studied it and am not a mathematician. Having said that,
# It seems to be the set of all numbers having the same number of bits as a starting
# number (the center) and differing from that number by at most (radius) bits. The
# code below assumes the starting number is also included, but I haven't confirmed
# that this should be the case. This is just me playing around with a quick hack.
#
# Another word used is "Hamming sphere" but I think this might be something different,
# namely: The set of all numbers having the same number of bits as a starting number
# (the center) and differing from that number by exactly (radius) bits.
# 
# This script calculates the Hamming ball according to the first definition above.
#

import os
import sys

def ball_for_number_with_bits_with_radius(number, numBits, radius):
    
    ball = ball_for_number(number, numBits)

    if radius == 1:
        return ball
    else:
        result = ball.copy()
        for neighbor in ball:
            items = ball_for_number_with_bits_with_radius(neighbor, numBits, radius-1)
            result = result.union(items)
        return result

        
def ball_for_number(number, numBits):
    ball = set()
    start = number & 0xFFFFFFFF # limit to 64-or-smaller-bit numbers
    ball.add(number)
    for n in range(0,numBits):
        mutated = number ^ 1<<n;
        ball.add(mutated)
    return ball


def legal_argument(arg):
    legal_args = 'nbr'
    if arg in legal_args:
        return True
    return False

def usage_exit():
    print("\nUsage: " + sys.argv[0] + " -n number -b bits -r radius")
    print(
"""
Options:
  -n  the starting number
  -b  how many bits to treat the number as (including left padding)
  -r  how many bit differences from the starting number to include
""")
    exit(-1)


def main():

    if len(sys.argv) < 7:
        usage_exit()

    try:
        if len(sys.argv) < 4 or not legal_argument(sys.argv[1][1]) or not legal_argument(sys.argv[3][1]) or not legal_argument(sys.argv[5][1]):
            usage_exit()
        if sys.argv[1].startswith('-') and sys.argv[1][1] == 'n':
            number = int(sys.argv[2])
        if sys.argv[1].startswith('-') and sys.argv[3][1] == 'b':
            numBits = int(sys.argv[4])
        if sys.argv[1].startswith('-') and sys.argv[5][1] == 'r':
            radius = int(sys.argv[6])
    except IndexError:
        usage_exit()

    if numBits > 64:
        numBits = 64
        print("warning: limited to 64 bits")

    limit = (2**(numBits+1))-1
    if number > limit:
        print("error: number " + str(number)
              + " is larger than " + str(limit)
              + ", the max value for " + str(numBits)
              + " bits.")
        sys.exit()

    ball = ball_for_number_with_bits_with_radius(number, numBits, radius)
    for item in ball:
        result = bin(item)[2:].zfill(numBits)
        print(str(item).zfill(8) + ": " + result)


if __name__ == '__main__':
    main()