feat: Introduce hamming code generator

bit_manipulation/hamming_code_generator.py

@@ -0,0 +1,98 @@
+"""
+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=0s
+    by 3B1B YT channel
+
+    Wikipedia:
+    https://en.wikipedia.org/wiki/Hamming_code
+
+    >>> hamming_15_11("00110001110")
+    '0010101110001110'
+    >>> hamming_15_11("10110000110")
+    '0101001100000110'
+    >>> hamming_15_11("10111100110")
+    '0011001101100110'
+    >>> hamming_15_11("10001000010")
+    '0001100001000010'
+    >>> hamming_15_11("00010abcdef")
+    "Input must be an 11-bit binary string containing only '0's and '1's."
+
+    """
+    is_bin = True  # assuming it's binary initially
+    for i in number:
+        if i not in ("0", "1"):
+            is_bin = False
+            break
+
+    if len(number) == 11 and is_bin:
+        digits = [int(number[i]) for i in range(len(number))]
+
+        total_num_1 = sum(digits)
+        hamming_digits = [0] * 16
+
+        parity_positions = {
+            1: [0, 1, 3, 4, 6, 8, 10],
+            2: [0, 2, 3, 5, 6, 9, 10],
+            4: [1, 2, 3, 7, 8, 9, 10],
+            8: [4, 5, 6, 7, 8, 9, 10],
+        }
+
+        redundant_bits = [0] * 5
+
+        redundant_bits_index = 1
+        for positions in parity_positions.values():
+            parity = 0
+            for idx in positions:
+                parity ^= digits[idx]
+            redundant_bits[redundant_bits_index] = parity
+            redundant_bits_index += 1
+
+        redundant_bits[0] = (
+            total_num_1 % 2
+            ^ redundant_bits[1]
+            ^ redundant_bits[2]
+            ^ redundant_bits[3]
+            ^ redundant_bits[4]
+        )
+
+        j = -1
+        r = 0
+        redundant_bit_locations = [0, 1, 2, 4, 8]
+        for k in range(16):
+            if k in redundant_bit_locations:
+                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 "Input must be an 11-bit binary string containing only '0's and '1's."
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()