ON NON-EXISTENCE OF PERFECT DOUBLE HAMMING-ERROR-CORRECTING CODES ON Q = 8 AND Q = 9 SYMBOLS

被引：2

作者：

ALTER, R

机构：

[1] System Development Corporation, Santa Monica

来源：

INFORMATION AND CONTROL | 1968年 / 13卷 / 06期

关键词：

D O I：

10.1016/S0019-9958(68)91038-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

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 y2 = 8k+1 + 17 and y2 = 2(9k + 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. © 1969 Academic Press, Inc.

引用

页码：619 / &