Error-Correcting Codes for Arithmetic Operations

The problem of finding arithmetic error-correcting codes for nonuniformly distributed errors (so-called error bursts) is of practical importance. Below we present several theorems that make it possible to find, either directly or by some sort of inspection, numbers that generate arithmetic error-correcting codes. The results are tabulated. The article presents the results of further work of the authors on the theory of arithmetic error-correcting codes and is a direct continuation of [E. T. Mironchikov and V. D. Kolesnik, Radiotekhn. Elektronika, 1963, vol. 8, no. 1, pp. 8–15]. The codes obtained are analogs of the corresponding Fire and Elspas–Short codes.