Here’s a generator matrix,
A parity check matrix for this, is one where (hence the product of with a codeword is also 0, though an error word generates a non-zero output).
Two candidates for this present themselves (are there others? I can’t see them):
Taking , there are distinct messages (codewords), where , but he generator can create different outputs. So we have non-zero code words and possible outputs, the number of detectable errors is:
The most likely error is the one with the lowest Hamming weight:
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