Accession Number : AD0680112

Title :   ON THE NON-EXISTENCE OF PERFECT DOUBLE HAMMING-ERROR-CORRECTING CODES ON q=8 AND q=9 SYMBOLS,

Corporate Author : SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF

Personal Author(s) : Alter,Ronald

Report Date : 05 NOV 1968

Pagination or Media Count : 19

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)

Descriptors :   (*CODING, CORRECTIONS), ERRORS, EQUATIONS, THEOREMS

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE