Sum codes with fixed values of multiplicities for detectable unidirectional and asymmetrical errors for technical diagnostics of discrete systems

We introduce the concept of sum codes with fixed values of the multiplicities of unidirectional and asymmetrical errors in data vectors. We show that such codes can be constructed on the basis of weighing one of the data vector's bits by a natural number $w\ge 2$ and then calculating the total weight of the data vector modulo the Berger code (${M=2^{\left\lceil \log _{2} \left(m+1\right)\right\rceil } }$). We establish the basic characteristics of the new class of sum codes. Compared with the Berger code, the proposed codes have the advantage of detecting symmetrical errors while maintaining the property of detecting any unidirectional and asymmetrical errors up to fixed multiplicities. Such codes can be effectively used in the construction of concurrent error-detection systems for combinational logic devices and, especially, in the construction of systems with the detection of all single faults in the controlled device.