hamming_code_generator.py

""""
Author: Ayush Chakraborty
Date: 6th October 2024

generate (15,11) hamming encoded bits gives 11 bit data 

input: 11 bit binary number with type string
return: 16 bit binary hamming encoded number returned in string form
"""

def hamming_15_11(number: str) -> str:
    """
    Performs parity checks to assign values to the redundant bits, in the 16 bit number
    returned, bits at index 0, 1, 2, 4, 8 are redundant bits used for checking

    Hamming generated 16 bits generated from the 11 bit binary number can only detect and change
    a single bit change, but can only detect more than a single bit change 
    
    for more theoretical knowledege about Hamming codes, refer: https://www.youtube.com/watch?v=X8jsijhllIA&t=143s
    by 3B1B YT channel

    >>> hamming_15_11("00110001110")
    '0010101110001110'
    >>> hamming_15_11("10110000110")
    '0101001100000110'
    >>> hamming_15_11("10111100110")
    '0011001101100110'
    >>> hamming_15_11("10001000010")
    '0001100001000010'
       
    """
    if len(number) == 11:
        digits = [0 if number[i] == '0' else 1 for i in range(len(number))]
        total_num_1 = sum(digits)
        hamming_digits = [0 for i in range(16)]
        bit_1 = reduce(lambda x,y:x^y, [digits[1], digits[4], digits[8], digits[0], digits[3], digits[6], digits[10]])
        bit_2 = reduce(lambda x,y:x^y, [digits[2], digits[5], digits[9], digits[0], digits[3], digits[6], digits[10]])
        bit_3 = reduce(lambda x,y:x^y, [digits[1], digits[2], digits[3], digits[7], digits[8], digits[9], digits[10]])
        bit_4 = reduce(lambda x,y:x^y, [digits[4], digits[5], digits[6], digits[7], digits[8], digits[9], digits[10]])
        bit_0 = int(total_num_1%2)^bit_1^bit_2^bit_3^bit_4

        redundant_bits = [bit_0, bit_1, bit_2, bit_3, bit_4]

        j = -1
        r = 0
        for k in range(16):
            if (k == 0 or k==1 or k==2 or k==4 or k==8):
                hamming_digits[k] = redundant_bits[r]
                r += 1
            else:
                j += 1
                hamming_digits[k] = digits[j]   

        return ''.join([str(i) for i in hamming_digits])
    
    else:
        return "please provide a 11 bit binary number"

if __name__ == "__main__":
    from functools import reduce
    import doctest

    doctest.testmod()