NON-BINARY ERROR CORRECTION CODES 



1351 



(base 5) channel. Each message will consist of ten information digits 

 and two check digits. 



Let .ri and xo represent the check digits, and x^ , Xt , ■ ■ • , Xn represent 

 the information digits. 



The equations for calculating .ri and X2 are: 



I.T1 + Oa-2 + 0.r3 + 1.1-4 + l.r5 + l.re + Ixj 



+ 2xs + 2x9 + 2xw + 2xu + 2x-i2 = mod 5, 

 Oxi + U-2 + 2.r3 + 1x4 + 2.1-5 + 3.1-6 + 4x7 



+ 0.r8 + I.T9 + 2.rio + 3.TU + 4.ri.- = mod 5. 



(4) 

 (5) 



At the decoder, the corrector terms, Ci and d , are calculated using x/, 

 the received value of Xi , in the following formulas: 



Ixi' + 0.1-2' + 0x3' + 1x4' + 1.1-5' + Ixe' + Ixt' 



+ 2x8' + 2x9' + 2xio' + 2xn' + 2xio' = ci mod 5, 



Ox/ + 1x2' + 2x3' + 1.1-4' + 2.1-5' + 3x6' + 4x7' 



+ Oxg' + Lrg' + 2.rio' + 3xu' + 4x12' = c^ mod 5. 



(6) 



(7) 



The values of C1C2 corresponding to the condition that one and only- 

 one digit is too high by 1, x/ = Xi -\- 1, can be read by reading the coeffi- 

 cients of the ith digit in the corrector formulas. This quantit}^ is therefore 

 the characteristic of the ith. digit. If x/ = Xj — 1, then the fiv^es com- 

 plements of these coefficients will be the value of the corrector. Table III 

 lists the characteristics and characteristic complements associated with 

 each digit. 



Table III — Characteristics and Characteristic Complements 



Systematic Quinary Code 



