dwight elvey commented on a post on Blogger.
Using a CRC to do a correction can be complicated but I have a method that is simple to use. Most break the polynomial into prime factors and use what is called the Chinese remainder theorem to do a forward search for the error syndrome. It is vary efficient for a hardware implementation but tedious for software.
First one must understand what a correctable error is. These CRCs and only correct one burst that is limited in length. I believe this one is 12 bits.
If there are multiple errors, that are greater in length, it is not correctable, using the CRC. If it is valued data, don't give up. You can often correct it if it is text or program by looking at it. Sometimes it helps to also know the encoding method as there may be a bitwise shift. I've fixed tapes this way in the past. You'll know when your right as the checksum or CRC will be right.
Back to the CRC, you'll see there is a number of 0's in the center of the CRC. If you play the CRC backwards ( requires slightly different coding ),
a bit at a time ( you can't use a bytewise table lookup CRC algorithm ) you
should find a point where only the center bits where the polynomial  has
the 0's has 1's in it. The is the error syndrome and can be used to XOR with the data bits to repair the data.
If you never find this, within the data block size, it means the error is not recoverable with the CRC.
I find that each time I do this, I have to do some experiments to get the
algorithm correct by using some good data with a known error.
Dwight
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