The issue in the case was whether Samsung infringed on the design Apple registered in 2004.
The lower court in July had declared Samsung's Galaxy computers "do not have the same understated and extreme simplicity which is possessed by the Apple design. They are not as cool."
In their ruling Thursday, all three justices who heard the appeal ordered Apple to publicize the court rulings to make sure consumers are not biased against Samsung.
Judge Robin Job wrote in the unanimous opinion: "The acknowledgement must come from the horse's mouth. Nothing short of that will be sure to do the job completely."
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