NON-BINARY ERROR CORRECTION CODES 



13G5 



mum of 6 — 7n{p — h) states are allowed for the adjustment digit. (For 

 certain values of the check digits, more states could be allowed, but a 

 code for utilizing these extra states becomes unwieldy.) For the case 

 b = 10, p = 11, this turns out to be 10 — m. At least one state must 

 be available for each adjustment digit, to have a workable code. 



The characteristic of an adjustment digit is determined in the follow- 

 ing way: if an adjustment digit adjusts the Jth check digit, then the^th 

 digit of the characteristic of the adjustment digit is 1 ; otherwise, it is 0. 

 The characteristic of all other digits may be derived using the rules de- 

 scribed above for the prime number base channel, except that p, the 

 prime number base of the code must be used instead of b, the number 



Table VI — Illustration of Adjustment Digit 



base of the channel, for generating characteristics. A message is initially 

 encoded using a value of for an adjustment digit. Subsec^uently, if the 

 adjustment digit always has at least q allowable states, it may be u.sed 

 to transmit one additional information digit, base q, of information. If 

 the value of this information digit is y, the (y + l)st lowest possible value 

 of the adjustment digit (making the lowest value equivalent to // = 0) 

 meeting the requirement that all adjusted check digits are no greater 

 than b — 1 is transmitted. The adjustment digit in conjunction with 

 its associated check digits conveys a digit, base q, of information. 



In the example given above, q = (S and if y is 4, the fifth lowest value 

 of ^0 , 7, is transmitted. The lowest ^'alue must be associated with y = 0. 

 The values of ZoZiZ2Z32i that are sent over the decimal chamiel are 75431. 



An example of such a code is one using a decimal channel working in a 

 unodecimal base for the purposes of encoding and error correction. The 

 word length, n, is twelve, nhie decimal information digits, one octal (base 



