If I recall right this depends on the original message length and 1 bit is a bit of an edge case. If you transfer just 1 bit, you're very space constrained and it's hard to do much. 1 bit to 1 bit has nothing, 1 bit to 2 bits has single-bit error detection, and 1 bit to three bits has single bit error correction (--and 2 bit error detection-- (this isn't right, thinking about it for a second)). After this, the minimum required checksum length growth logarithmically, plus 1 or 2 for detection / correction - and that constant factor makes 1 bit so weird.