feat: Introduce hamming code generator #11827
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| """ | ||||||
| Author: Ayush Chakraborty | ||||||
| Date: 6th October 2024 | ||||||
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| generate (15,11) hamming encoded bits gives 11 bit data | ||||||
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| input: 11 bit binary number with type string | ||||||
| return: 16 bit binary hamming encoded number returned in string form | ||||||
| """ | ||||||
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| 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 | ||||||
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| 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 | ||||||
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| for more theoretical knowledege about Hamming codes, refer: | ||||||
| https://www.youtube.com/watch?v=X8jsijhllIA&t=0s | ||||||
| by 3B1B YT channel | ||||||
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| Wikipedia: | ||||||
| https://en.wikipedia.org/wiki/Hamming_code | ||||||
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| >>> 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." | ||||||
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| """ | ||||||
| is_bin = True # assuming it's binary initially | ||||||
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AyushChakraborty marked this conversation as resolved.
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| for i in number: | ||||||
| if i not in ("0", "1"): | ||||||
| is_bin = False | ||||||
| break | ||||||
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| if len(number) == 11 and is_bin: | ||||||
| digits = [int(number[i]) for i in range(len(number))] | ||||||
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| total_ones = sum(digits) | ||||||
| hamming_digits = [0] * 16 | ||||||
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| 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], | ||||||
| } | ||||||
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| redundant_bits = [0] * 5 | ||||||
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| 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 | ||||||
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| redundant_bits[0] = ( | ||||||
| total_ones % 2 | ||||||
| ^ redundant_bits[1] | ||||||
| ^ redundant_bits[2] | ||||||
| ^ redundant_bits[3] | ||||||
| ^ redundant_bits[4] | ||||||
| ) | ||||||
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| data_index = 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.pop(0) | ||||||
| else: | ||||||
| hamming_digits[k] = digits[data_index] | ||||||
| data_index += 1 | ||||||
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| return "".join([str(i) for i in hamming_digits]) | ||||||
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| elif len(number) != 11 or not is_bin: | ||||||
| return "Input must be an 11-bit binary string containing only '0's and '1's." | ||||||
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| else: | ||||||
| return "Invalid input" | ||||||
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| if __name__ == "__main__": | ||||||
| import doctest | ||||||
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| doctest.testmod() | ||||||
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