Arithmetic Codes with Correction of Multiple Errors

The use of arithmetic correcting codes in a system consisting of a communication channel and a digital computer makes it possible to detect or correct errors arising in any section of this system, both in the communication channel and in the information processors, and this affords the possibility of considerably reducing the number of encoders and decoders. The universality of arithmetic codes is due to this. Methods of finding such codes with code distance equal to three are described in the literature. An extremely inefficient inspection process may be used for finding codes with a large distance. In this paper a method of synthesizing arithmetic codes with any code distance is presented. Several theorems enabling this synthesis to be realized are stated. An upper bound is given for arithmetic codes similar to Hamming's upper bound for group codes.