On the Non-Existence of Perfect Double Hamming-Error-Correcting Codes On Q=8 and Q=9 Symbols.

摘要

This work is a continuation of an earlier paper by the author where a similar result is achieved for the value q = 7. By generalizing and extending the techniques developed in this earlier paper the diophantine equations y squared = 8 to the (k+1) power + 17 and y squared = 2 x (9 to the kth power) + 7 are shown to have no solution in integers for k > 2. Since this is a necessary condition for the existence of perfect double Hamming-error-correcting codes on q = 8 and 9 symbols respectively, it follows that there exist no such codes. (Author)