I have found a lot of material on error correcting codes from the 70s and 80s. Most of these codes do not work for arithmetic operations such as addition. I was able to solve bi-residue codes that can do one bit error correction (provided only one bit flip is in the result). However this is not useful if error is in carry as this results in an error of amount '2^n + 1' from the original answer.
Many papers mention that cyclic AN codes can correct such error due to larger distance/weight of codes. However, I have never found an example where this is shown with actual numbers. Does anyone have an idea of how these codes work? As a test case we have assume the following radix-2 numbers: '11' and '01'. We assume that '01' became '00' as a result of bit flip and result changed from '100' to '11'.