Looking for software suggestions

[Labster]

If you waste some of your bytes on checksums or hashes (make the archive a little larger), you can do it.  This would also verify that your archive is not corrupted, so it is useful anyway.  So, for instance, .ZIP uses the CRC-32 algorithm to check for correct data, and you can use it for error correction.  Basically it's extra information, so you can try to reconstruct which bitflips would result in the correct CRC.

Cyclic redundancy checks (CRCs) can correct 1-bit errors for messages at most 2^(n-1)-1 bits long for optimal generator polynomials of degree n, see Mathematics of cyclic redundancy checks#Bitfilters

I'm not a computer scientist so I have no idea how to explain this further, but as a software engineer it's good to know what's possible.