On the Non-Existence of Close-Packed Double Error-Correcting Codes on Q=7 Symbols

摘要

The diophantine equation 2y squared=((7 raised to the kth power)+1) is shown to have no solutions in integers for k > 2. Since this is a necessary condition for the existence of close-packed double error-correcting codes on q = 7 symbols, there exist no such codes. (Author)