For each of the following group codes, (i) determine the minimum distance between code words; (ii) determine the maximum number of errors that can be reliably detected, and (iii) determine the maximum number of errors that can be reliably corrected. (a) C_1 = {(000000), (100110), (010101), (001011), (110011), (011110), (101101), (111000)} in ?_2^6. (b) C_1 = {(000 000 00), (100 101 10), (010 011 10), (001 110 01), (110 110 00), (011 101 11), (101 011 11), (111 000 01)} in ?_2^8.
Added by Janice C.
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To do this, we will find the Hamming distance between each pair of code words and take the minimum of these distances. Hamming distances: (000000, 100110) = 3 (000000, 010101) = 3 (000000, 001011) = 3 (000000, 110011) = 3 (000000, 011110) = 4 (000000, 101101) = Show more…
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