Construction of Single-Error-Correcting Nonbinary Arithmetic Codes

The authors solve the problem of determining a fundamental characteristic of a single-error-correcting $AN$-code, namely the quantity $M_r(A,3)$, which is defined as the minimum positive integer, the weight of whose product by $A$ in the base $r$ number system is less than 3. The proposed method can be used for any $r$. Expressions are given for the computation of $M_r(A,3)$ when $r=5,7,11$, and 8.