On summation code properties in functional control circuits

Modular sum codes in building testable discrete systems

“…5. Any SM(m,k)-code does not detect the same fraction of errors of d multiplicity in code data vectors of the total number of errors of this multiplicity if d<M. 6. The value of d factor approaches the value d for Berger code with increasing of M value for any SM(m,k)-codes [6]:…”

“…At the system design phase the operational functions of controlled unit are matched with the length of data vector, m, and the outputs of controlling unit -with the length of check vector, k. During the process of system operation the single faults of controlled unit can result in the distortions of bit values of data vector with different multiplicities d. The capability of system to detect the errors in controlled unit is also depend on (m,k)-code characteristics. Thus, it is possible to consider the characteristics of certain (m,k)-code based on the error detection in data vectors, studying by this the features of the discrete system itself [6].…”

“…The number of bits in check vector of these codes can be determined by the following formula These codes, among all of the SM(m,k)-codes, has the minimum total number of undetecta-978-1-4673-7776-8/15/$31.00 ©2015 IEEE ble errors in data vectors. Its number can be calculated using the following formula[6]:…”

On codes with summation of data bits in concurrent error detection systems

“…S(n, m)-codes have an important property [11]: for every Berger code, the fraction of undetectable errors in data bits of multiplicity d of the total number of errors in data bits of this multiplicity does not depend on the number of data bits and is a constant…”

Providing Reliability of Physical Systems: Partially Programmable Circuit Design

“…Then we change the fault circuit for the fault free one. Besides that, we may apply fault tolerance circuits using self-checking circuits and checkers [1][2][3]. Unfortunately, these methods are connected with the essential structural overhead (exceeding 100%) often unacceptable in practice.…”