Quiz

However, this turned out to be a rather difficult example. Perhaps someone will find a simpler solution.

Let's see what we can do now.

Added 17 minutes later
Yes, indeed, the example is not easy, but let's still try to encode and transmit the combination
1110

b₁=1
b₂=1
b₃=1
b₄=0
b₅=1
b₆=1
b₇=1

That is, 1110111
So, if we received 1110111, it means he sent 1110 and no bit was corrupted.

Now let's try to encode and transmit the combination
1101

b₁=1
b₂=1
b₃=1
b₄=0
b₅=0
b₆=1
b₇=1

That is, 1110011

What if he was actually transmitting 1101, and not 1110, and the fifth bit was simply corrupted from 0 to 1?

Now I'll just check myself to make sure I calculated everything correctly.

Added 3 minutes later
It seems correct, but the example is indeed not easy. :)