Near-Perfect Codes for Binary-Coded Radix-r Arithmetic Units

This paper considers AN arithmetic codes with radix r > 2 and binary-coded digits (BCr) using weights. The error-correcting capability of the AN codes is single bit within any BCr digit, that is, the corrected errors are of the form ± wirj where wi are the weights of the BCr code. The paper characterizes a class of AN codes having a generator of the form A = r · p where r|r − 1 or τ|r + 1 and p prime is greater than r − 1 or r + 1. It is shown that these codes, under certain conditions, are near perfect.