The decision made in the US District Court for the Western District of New York could prove costly for Sun when the jury reconvenes to determine damages this week.
Kodak has indicated that it will ask Sun for $1,06bn in lump-sum royalties, according to a local press report.
Kodak initially sued Sun in 2002, claiming that, during Sun's development of its Java programming language, the company had violated three patents issued in the mid-1990s.
Sun originally dismissed the claims as without merit. Sun representatives were not immediately available to comment on the case.
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