feat: Introduce hamming code generator

Introduced a new .py file which generates 16 bit
hamming codes from the given 11 bit input.
Additional 5 bits are redundant, used to correct
single bit errors within the data bits

Author: AyushChakraborty

bit_manipulation/hamming_code_generator.py

@@ -0,0 +1,65 @@
+""""
+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()
+
+