Nonbinary Arithmetic Correcting Codes

A method is considered for synthesizing arithmetic separable codes with error correction in one position for nonbinary positional systems of calculation. To construct the codes the theory of second-degree congruences is used in conjunction with the elements of group theory. Theorems are given for determining the various $r$-ary codes analytically. The relation between $r$-ary and $r^s$-ary codes is used to construct codes with correction of groups of errors in the $r$-ary system of calculation. A number of modules are found which generate correcting codes for calculation systems with bases $r=3,4,\dots,10,16$.