1306 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



8) information digit a.ssociated with the adjustment digit, and two check 

 digits. The characteristics are the following: 



Let 2ii and 212 represent the vahies of the check digits .Th and Xio , 

 originally derived from .Ti , X2 , • • • , Xs , x^ : 



Xi + X2 + Xz + 



7.ri + 9.r.2 + 8.r3 + • 



• + Xg = —Zn mod 11, 

 + 2.r9 = —Zn mod 11. 



(43) 

 (44) 



From Zn and 212 , the ten different words (0, Zn , 212), (1, ^n — 1, 212 — 1), 

 (2, Zn — 2, Z12 — 2), • • • , (9, Zn — 9, Zn — 9) are formed. If y is the 

 value of the octal information digit, the {y + l)stsuch word, that does 

 not contain the digit 7, is selected and transmitted as the last three 

 digits of the message. For example, if ^u = 2, Zvi = 1 and y = Q, the ten 

 words are (0, 2, 1), (1, 1, 0), (2, 0, 7), (3, 7, 9), (4, 9, 8), (5, 8,7), (6, 7, 6), 

 (7, 6, 5), (8, 5, 4), (9, 4, 3); the word (8, 5, 4) is selected since it is the 

 seventh in the secjuence that does not contain any 7's. Table VII shows 

 the choice of the three last digits as a function of y, given 2:11 = 2, 212 = 1. 

 Formula (45) is used for calculating the corrector. Let C> represent 

 the jth digit of the characteristic of Xi , Cy the jth digit of the cor- 

 rector, and Xi the received value of Xi . Then, 



12 

 Cj = ^ Cijx/ mod 11. (45) 



The translation from corrector to correction is the same as if the original 



Table VII 



Relation Between Adjusted Digit and 

 Associated Information 



il 



