; or (D) has a student enrollment in which more than 50 percent of the students either do not have a secondary school diploma or its recognized equivalent, or do not meet the requirements of section 484(d), and does not provide a 2- or 4-year program of instruction (or both) for which the institution awards an associate’s degree or a bachelor’s degree, respectively, except that the Secretary may waive the limitation contained in this subparagraph if an institution demonstrates to the satisfaction of the Secretary that the institution exceeds such limitation because the institution serves, through contracts with Federal, State, or local government agencies, significant numbers of students who do not have a secondary school diploma or its recognized equivalent or do not meet the requirements of section 484(d). (c) List of accrediting agencies For purposes of this section, the Secretary shall publish a list of nationally recognized accrediting agencies or associations that the Secretary determines, pursuant to subpart 2 of part H of title IV, to be reliable authority as to the quality of the education offered. (d) Certification The Secretary shall certify, for the purposes of participation in title IV, an institution’s qualification as an institution of higher education in accordance with the requirements of subpart 3 of part H of title IV. (e) Loss of eligibility An institution of higher education shall not be considered to meet the definition of an institution of higher education for the purposes of participation in title IV if such institution is removed from eligibility for funds under title IV as a result of an action pursuant to part H of title IV. (f) Rule of construction Nothing in subsection (a)(2) relating to State authorization shall be construed to— (1) impede or preempt State laws, regulations, or requirements on how States authorize out-of-State institutions of higher education