Consider the binary linear code Use nearestneighbor decoding

Consider the binary linear code

Use nearest-neighbor decoding to decode 11101 and 01100. If the received word 11101 has exactly one error, can you determine the intended code word? Explain your reasoning.

Solution

The received word 01100 is one error off from the codeword 11100 so nearest-neighbor decoding would decode it as 11100. For the received word 11101 we cannot correct one error. Both the codeword 111000 and the codeword 11001 are distance one from the received word so we cannot tell which is the correct codeword. (Note the weight of this code is 2 so this code should not always correct 1 error.)