Ernest L. Wilkinson, 79, founder of the Washington law firm of Wilkinson, Crugan and Barker and former president of Brigham Young University, died of cardiac arrest Thursday in Salt Lake City, Utah.

He was president of the university in Provo, Utah, from 1951 to 1971, taking time out in 1974 to run unsuccessfully for the U.S. Senate.

Born in Ogden, Utah, Mr. Wilkinson graduate from Brigham Young University and received a law degree in 1926 from George Washington University. He earned a doctor of juridical science degree from Harvard University a year later.

While attending George Washington University, he taught history at the old Business High School here. After working and teaching in New York and New Jersey, he returned to Washington in 1935 to establish a law firm with Walter G. Moyle.

Following World War II, he founded the law firm of Wilkinson, Cragun and Barker, which now has approximately 40 lawyers. He remained asociated with the firm until his death. A brother, Glen, is senior partner.

Mr. Wilkinson received wide recognition in the early 1950s for the large judgment he had obtained on behalf of the Ute Indians against the United States as payment for tribal lands seized in 1880. The judgment was for approximately $32 million. Mr. Wilkinson had worked on the case from 1935 to 1950.

He also handled litigation for other American Indian tribes and played a key role in bringing about the enactment of the Indian Claims Commission Act.

Active for many years in the Mormon Church, he served as counselor in the Washington, D.C., Stake Presidency.

While at Brigham Young, he had seen the university enrollment increase from 4,000 to 25,000. He also was administrator of the church education system of the Mormon church.

He had been a member of the D.C., Utah and American bar associations. He had been a delegate to the White House Conference of Education; was a member of the U.S. Chamber of Commerce, and an overseer of the Freedom Foundation at Valley Forge. He was a former president of the National Right to Work Legal Defense Foundation and of the American Association of Presidents of Independent Colleges and Universities.

In addition to his brother, Glen, of Washington, he is survived by his wife, Alice Ludlow Wilkinson, of the home in Salt Lake City; three sons, Dr. Ernest L., David L. and Douglas D. and two dayghters, Alice Anderson and Marian Jensen, all of Salt Lake City; another brother Woodrow, of Salt Lake City, 15 grandchildren and two great-grandchildren.