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There is nothing in the Code of Canon Law which requires a wait of any particular time after a death for a funeral to take place. (My father was buried two days after his death; so were my wife's parents. In all cases the delays were simply due to the need to coordinate with the priest and the funeral home.)
The Catechism of the Catholic Church does briefly allude to the idea that the community may celebrate "the anniversary of a death, or the seventh or thirtieth day after death" (paragraph 1687); I've never seen such a celebration.
The Ordo Exsequiarum (Order of Funerals, the book which contains the Catholic rites surrounding funerals) may have something further to say on this; unfortunately, it is not a text to which I have access.