Magic Card Tricks on Hamming Codes over Finite Fields

Magic tricks based on binary Hamming codes are well known. A typical trick goes as follows. The audience picks a number from 0 to 15. The magician prepares seven Tables and asks Yes/No questions—if the number is in each Table—to the audience whose response may include at most one lie corresponding to an error of the code. Nevertheless, the magician can guess the correct number picked. This trick is introduced in [1] with a fascinating device so that the magician can easily make a performance. The same trick is discussed with the improved device in [3], and without device in [4]. Another interesting trick is discussed in [2]. In this article we generalize binary tricks to present magic card tricks based on Hamming codes over finite fields of 3, 4, and 5 elements.