How Can I Devise a Code for Digits 0-9 with a Hamming Distance of 2?

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The discussion focuses on devising a 7-bit code for the digits 0 to 9 that maintains a Hamming distance of 2. The participant initially attempted to use binary representations of the digits but encountered challenges when transitioning from 0-7 to 8-9. It was established that three redundancy bits are necessary to achieve a Hamming distance of 2, which allows for the correction of single-bit errors. The conclusion emphasizes that a total of 7 bits is required to represent the digits 0 through 9 effectively.

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*Devise a code for the digits 0 to 9 whose Hamming distance is 2.*

My efforts to answer this problem are kind of hard to explain, but I'll try. First I wrote out the digits 0 to 9 in binary. Then I tried to find a number that was only 2 numbers different from each one (get 2 ones when XOR them), but there was no single code that worked for all 9 numbers. I found one that worked from 0 to 7, but once the digits changed to 1000 it didn't work anymore.

Am I even approaching this right? Please help.
 
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You need 3 redunancy bits for a distance of 2, which allows you to correct single bit errors. Since it takes 4 bits to represent the numbers 0 through 9, you need a 7 bit code.
 

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