Separate Non-Homomorphic Checking Codes for Binary Addition.

摘要

In this paper,necessary and sufficient conditions for successful detection of errors in a binary adder by any separate code are developed. The author demonstrates the existence of separate checking codes for addition modulo (2sup n) ( n >or = 4) and modulo (2sup n) -1 (n > 5, n even),which are not homomorphic images of the addition being checked. A non-homomorphic code is constructed in a regular fashion from a single check symbol with special properties. Finding all such initial check symbols requires an exhaustive search of a large tree,and results indicate that the number of distinct codes for a particular modulus grows rapidly with n. In an appendix,the author examines a modulo (2sup n) adder where the carry out of the high position is also presented to a checker. (Modified author abstract)