NON-BINARY ERROR CORRECTION CODES 



1375 



Table XII 



Binary Code used for Correcting 

 Decimal Message 



Parity Check Digt 

 Parity Check Digit 



Parity Check Digit 



Parity Check Digit 



Position in Decimal Message 



inary comp. 

 inary comp. 

 inary comp. 

 inary comp. 

 inary comp. 

 inary comp. 

 uinary comp 

 inary comp. 

 uinary comp 

 uinary comp 

 uinary comp 

 uinary comp 

 uinary comp 

 uinary comp 



of Lst digit 

 of 2nd digit 

 of 3rd digit 

 of 4th digit 

 of 5th digit 

 of 6th digit 

 . of 7th digit 

 of 7th digit 

 . of 6th digit 

 . of 5th digit 

 . of 4th digit 

 . of 3rd digit 

 . of 2nd digit 

 . of Lst digit 



To illustrate the method completely, a strictly binary example will 

 first be illustrated, then a related decimal example. In column a of Table 

 XII, the digits of a binary message are indicated and in column b, the 

 binary and quinary information digits. The values of the parity check 

 digits, which are shown in parentheses, are calculated by the usual for- 

 mula. Let Cij represent the jth digit of the characteristic of the fth 

 digit (including parity check digits) : 



14 



X) XiC.j = mod 2. 



(52) 



i=l 



This formula applies for all values of j and in this case will yield four 

 implicit eciuations each with one unknown term, the value of the parity 

 check digit. Using the given values of the binar}^ information digits, 

 the values of the parit}^ check digits are calculated. These are shown in 

 parentheses in Table XII. 



