NON-BINARY ERROR CORRECTION CODES 1379 



Note that the associated binary codes for performing such a correc- 

 tion must have the property that two binary digits may be corrected 

 since an error of ±2 corresponds to incorrect values for two associated 

 binary digits. If the noise is such that errors of ±2 are not very unhkely, 

 it may be desirable to place the binary and the quinary components of 

 any one decimal digit in a different binary error correction code word so as 

 to make the errors independent. In a seven decimal digit message, as an 

 example, the quinary components of the first four decimal digits can be 

 used to generate parity check digits which are conveyed by the binary 

 components of the last three decimal digits. The binary component 

 of the fourth decimal digit (this might be Be) and the ciuinary com- 

 ponents of the last three decimal digits generate parity check digits 

 conveyed by the binary components of the first three decimal digits. 

 Two separate binary error correction code messages are then conveyed 

 by a single seven digit decimal code message. Each message is in a four 

 information digit, three parity check digit Hamming Code. Through the 

 use of this code, one error in the binary component of any decimal digit, 

 and one error in the quinary component of any decimal digit may be 

 corrected. 



In certain cases, the quinary digits themselves might be encoded in an 

 error correction code for single unrestricted errors before the binary 

 process is carried out. This is helpful chiefly for occasional large errors, 

 leading to initial miscorrections. 



The variations based upon the principles described, which can be 

 applied to any channel, provided 6^4, including the pyramiding of one 

 code scheme upon another, are almost endless. Generally, the last 

 encoding and first decodhig step should be able to correct many more 

 errors than the first encoding step. For example, if quinary components 

 are encoded in single unrestricted error correction quinary code, the bi- 

 nary code should probably be a triple or quadruple error correction code; 

 otherwise a correction may not correspond to the most probable error 

 condition, and the correction scheme loses its effectiveness. 



These techniques cannot be conveniently applied to the ternarj^ chan- 

 nel, since a ternary digit cannot be resolved into two components effi- 

 ciently. 



6.2 Multiple Small Error Correction Codes 



One limitation of the above techniques is the requirement for a sys- 

 tematic binary code; i.e., a code in which some of the binary information 

 digits are transmitted directly, and others are determined by paritj'' 

 checks on information and previously calculated check digits. These 



