Description

Code from the previous stage works but is ineffective because every byte contains only 3 significant bits. All the rest is just an overhead to reliably send the message.

In this stage, we will use a more efficient code, the Hamming code. In this code, every byte contains 4 significant bits, and the other 4 bits are used as an overhead (well, only 3 of them are used as an overhead, the last one just isn't used).

To better understand how this code works, watch this video.

We will use the Hamming code [7,4], i.e. will write 7 bits, 4 of them would be significant bits, 3 of them would be parity bits and the last one would be unused (it should always be set to zero). Note that the video showed the Hamming code [12, 8] with 12 bits which contain 8 significant bits. You should use a smaller version of the Hamming code (just throw away from 9th to 12th bit from the video).

What should you do if the error occurs twice within a single byte? In our program, it won't happen since you simulate a single error in each byte. However, in real life, it definitely can happen. In telecommunications, all messages are split into packages. If errors in the package can't be corrected then this package should be retransmitted.

Examples

The greater-than symbol followed by a space (> ) represents the user input. Notice that it's not part of the input.

Example 1:

Write a mode: > encode

send.txt:
text view: Test
hex view: 54 65 73 74
bin view: 01010100 01100101 01110011 01110100

encoded.txt:
expand: ..0.101. ..0.100. ..0.110. ..0.101. ..0.111. ..0.011. ..0.111. ..0.100.
parity: 01001010 10011000 11001100 01001010 00011110 10000110 00011110 10011000
hex view: 4A 98 CC 4A 1E 86 1E 98

Example 2:

Write a mode: > send

encoded.txt:
hex view: 4A 98 CC 4A 1E 86 1E 98
bin view: 01001010 10011000 11001100 01001010 00011110 10000110 00011110 10011000

received.txt:
bin view: 01011010 10001000 10001100 01001110 00010110 10100110 00111110 10010000
hex view: 5A 88 8C 4E 16 A6 3E 90

Example 3:

Write a mode: > decode

received.txt:
hex view: 5A 88 8C 4E 16 A6 3E 90
bin view: 01011010 10001000 10001100 01001110 00010110 10100110 00111110 10010000

decoded.txt:
correct: 01001010 10011000 11001100 01001010 00011110 10000110 00011110 10011000
decode: 01010100 01100101 01110011 01110100
hex view: 54 65 73 74
text view: Test