Forty-four years late and 10 years after his death, Capt. Joseph Rochefort finally received his medal yesterday.

President Reagan presented the posthumous Distinguished Service Medal and a citation to his children at a White House ceremony. Rochefort, who broke a pivotal World War II Japanese code, enabling the U.S. Navy to predict and win the Battle of Midway, was recommended for the medal twice when he was alive, but it was denied him.

"I feel this is something that should have happened in his lifetime," his daughter Janet Elerding said after the ceremony. "I think he was probably very hurt at the time."

"We were giving an award that was 44 years overdue," said Rear Adm. Donald Showers, who served with Rochefort in 1942 and has spent the last 3 1/2 years lobbying for the medal.

Working as a Navy cryptologist in Hawaii in the months after the attack on Pearl Harbor, Rochefort predicted the massive Japanese fleet would attack the Midway Islands, a small U.S. outpost west of Hawaii. Naval intelligence workers in Washington, however, believed the attack would come two weeks later than Rochefort's estimate and that the target would be the Johnston Atoll or the West Coast of the United States.

But Pearl Harbor commander Adm. Chester Nimitz followed Rochefort's advice, surprising the Japanese and putting them on the defensive for the rest of the war.

After Midway, Nimitz recommended Rochefort for the medal, but Washington Navy brass denied it, claiming Rochefort was only one of the people contributing to the victory. Rochefort was soon transferred to San Francisco and assigned to command a floating dry dock. When Nimitz again requested the award in 1958, the Navy said World War II medal honors were no longer being considered.

Rochefort's supporters say he was denied the award and transferred to San Francisco because of Navy infighting.

Yesterday, Vice President George Bush, Defense Secretary Caspar Weinberger and Adm. William Crowe, chairman of the Joint Chiefs of Staff, watched while an aide read the citation praising Rochefort's "unrelenting efforts" to break the code. Reporters were not allowed to cover the ceremony.

"I had certainly hoped for it," Rochefort's son, retired Army colonel Joseph Rochefort Jr., said afterward. "I can't say I really thought it would happen. I'm more pessimistic than other people."

Rochefort said his father never expressed bitterness about not getting the medal.

"My father kept those things mostly to himself," he said. "He didn't complain. He thought there were other things far more important than that -- getting the war over with as quickly as possible. I never heard him complain that he didn't get what was coming to him."