The rule is as followed
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If a manufacturer has assigned a barcode then you are required to add this info in the GTIN field. Alongside the brand value with identifier exists to yes.
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If the manufacturer has not assigned a barcode, then remove the values brand, mpn and gtin and set identifier exists to no.
Here is a guide how to apply the rules using feed rules: https://support.google.com/google-ads/community-video/216954171
More info:
https://support.google.com/merchants/answer/6324351
https://support.google.com/merchants/answer/6324461
https://support.google.com/merchants/answer/6324482
https://support.google.com/merchants/answer/6324478