S.D. Codified Laws § 62-4-12
The amount of compensation which shall be paid for an injury to the employee resulting in death, if the employee leaves a spouse, child or children, shall be paid at the rate provided by § 62-4-3 for life or until remarriage in the case of a spouse. If the spouse remarries, two years' benefits shall be paid to the spouse in a lump sum. The amount of compensation which shall be paid for an injury to the employee resulting in death, if the employee leaves any children and no spouse, shall be paid at the rate provided by § 62-4-3 until the child is age eighteen or for life in the case of any child who is physically or mentally incapable of self-support or until age twenty-two for any child enrolled as a full-time student in any accredited educational institution. If any child is not in the custody of the surviving spouse, the compensation shall be divided pursuant to the provisions of § 62-4-12.1.
SDCL 62-4-12