Major Kardouk was the commander at the Fortress of Bakhine, where Professor Calculus was imprisoned by the Bordurian secret police under order of Colonel Sponsz.
History
Kardouk as seen in the book series
Kardouk authorised Calculus's release after Tintin and Captain Haddock, in disguise, visited Bakhine with the proper papers for his release, which they had previously stolen out of Sponsz's jacket in Bianca Castafiore's dressing room at the opera house in Szohôd.
After Sponsz realised that Kardouk had released Calculus, he ordered him to recapture him or else he would be shot, an order which he failed to enforce. It is unknown whether Kardouk was in fact killed for this or not.