Texts: a=1, b=2, c=3 but this hardly constitutes a code; anyone can figure it out. Obviously 8512 1215 spells "hello". A better code can be made by taking the numbers we just obtained, forming column vectors out of them, and then pre-multiplying them by some appropriately sized matrix, call it A. For example, I could code the message 2 3 4 5 177 2 2 4 -3 6 5 128 2 5 -6 7 12 127 (6) 4 5 -6 7 8 12 174 2 7 8 10 15 380. The vector on the right, the coded message, could be sent to its intended destination. Should the message be intercepted, it would be difficult to decipher without knowing the dimensions and elements of the coding matrix A. The original message can be retrieved by the receiver by pre-multiplying the coded message by the inverse of A (so it is important that the coding matrix A be invertible). Based on this approach, decode the message given by the numbers: 17, 15, 29, 15, 17, 29, 16, 31, 47, 6, 19, 20, 35, 24, 39, 14, 19, 19. If (7).
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