A class of A(N + C) codes and its properties

We discuss here a new class of arithmetic codes, called A(N + C) codes where A and C are constant positive integers, N is information to be coded. A(N + C) codes are a special case of AN + B arithmetic codes which were first studied by Brown. AN codes are linear and cannot be used to detect unidirectional multiple errors. A(N + C) codes are nonlinear and are useful for detecting and/or correcting symmetric errors, arithmetic errors and unidirectional errors. Furthermore, A(N + C) codes can be constructed to provide constant-weight, self-complementing and cyclic-code properties. It is apparent that the codes with these properties have, in some sense, broader capabilities of error detection and error correction.