https://www.epo.org/en/service-support/faq/searching-patents/asian-patent-information/korea/general-information-about-ip-3
Can computer software be patented in Korea?
Yes, but only if the software is recorded on a storage medium (CD-ROM, disc, etc.) and the combination of software and hardware as a whole represents an improvement over the prior art, has a technical result and constitutes a complete technical solution.
You can however get copyright protection for your software under the Copyright Act.
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