Aliens and xor

Other aliens?

Please hand a solution to this problem on Friday, November 12, 1999.

Assumptions here

  • 40% of the words are 111111. Abbreviate this word with Q. It is six bits long.
  • 30% of the words are 11001100. Abbreviate this word with S. It is eight bits long.
  • 20% of the words are 00000. Abbreviate this word with R. It is five bits long.
  • 10% of the words are 0101010. Abbreviate this word with T. It is seven bits long.

    Each message will be about 100 bits long. Below is the xor of two messages. Reconstruct both messages from this information.

    The xor of two bits: 0 indicates agreement; 1 indicates disagreement.

    Ciphertext

    00000 01111 10001 10011 00110 10101 10000 01001 10010 01100 01010 00010 10011 00111 11110 01100 10110 01001 01011 11001 1