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It wasn’t until the 1980s, when the code-breakers’ intelligence was declassified, that Mr. Showers spearheaded an effort to finally get the captain the honor he deserved. In 1985, nine years after his death, Rochefort was given the Distinguished Service Medal.

In a ceremony at the White House, President Reagan presented the award to Rochefort’s two children.

Nimitz said, ‘Had it not been for the excellent intelligence I was given, we would have read about the capture of Midway in the morning newspaper,’” Mr. Showers recalled. “And that’s absolutely true.”