ON THE NON-EXISTENCE OF PERFECT DOUBLE HAMMING-ERROR-CORRECTING CODES ON q=8 AND q=9 SYMBOLS,
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 05, 1968
- Accession Number
- AD0680112
Entities
People
- Ronald Alter
Organizations
- System Development Corporation