Generating local EAN barcodes

Hello experts,

We make some local products. To sell those in the market, we generate local barcodes for them.

EAN13 is the most used barcode in our region, that's why I developed my system to generate the first 12 digits of the barcode from some item information like number and date of release. The 13th  digit is the key and it generates using it's standard algorithm which is available and known.

I have faced a problem with some hyper markets (like Carrefour) that their systems didn't accept some of my locally generated barcodes.

The question:

Are there any rules for those barcodes which let Carrefour to reject my generated ones?
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Why are they rejecting them? What barcode types do they accept? UPC?
MuhajreenAuthor Commented:
They accept EAN13, most of barcodes are accepted, few are rejected.
If they can tell you why they are being rejected, I might be able to provide some suggestions.
MuhajreenAuthor Commented:
Actually even they do not know about their system> They are users, not developers.

My question is about EAN13 rules.
This should be what you need, especially the part about the check digit calculation.
Other than an invalid check digit, the image quality could be the issue. Could you attach a scanned  image of the barcodes that are failing?

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