Message Delivery

When delivering binary messages, Chris has a bad habit to turn off some set bits. To ensure that Bob does not receive the wrong message, both Alice and Bob agrees on a checking scheme - Alice will send two messages, one consists of the original message and the other one stores the amount of off bits in binary. For example, the message 0100100 1 0 0 1 0 will be compiled into (010010 , 100)(0 1 0 0 1 0 \text{ , } 1 0 0) because the original message has 4 off bits, the check bits will be 100100, which is 4 in decimal.

Now, Bob received the following compiled message (10011000010100 , 1001)(1 0 0 1 1 0 0 0 0 1 0 1 0 0 \text{ , } 1 0 0 1)

Which option bests describe the compiled message sent to Bob?

Details and Assumptions

  • It is possible for Chris to turn off the set bits in the check bits as well.
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