# What's the shortest possible code that correct all the single bit errors?

Suppose the original code is a 2-bit binary coding with 3 possible alphabet. \begin{align} a&\rightarrow 00\\ b&\rightarrow 10\\ c&\rightarrow 11 \end{align}

Is that $$\operatorname{Hamming}(7,4)$$ coding? Isn't 7-bit too long?

• Hint: look into repetition coding.
– MBaz
Dec 16 '20 at 14:48
• Like, repeat 3 times? So it's 6 bits long？I'm not sure if it has the same property with hamming code... Dec 16 '20 at 17:55