BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CSL-TR-72-35
       ENTRY:: December 01, 1994
ORGANIZATION:: Stanford University, Computer Systems Laboratory
       TITLE:: SEPARATE NON-HOMOMORPHIC CHECKING CODES FOR BINARY ADDITION
        TYPE:: Technical Report
      AUTHOR:: Kolupaev, Stephen G.
        DATE:: July 1972
       PAGES:: 28
    ABSTRACT:: In this paper, necessary and sufficient conditions for
               successful detection of errors in a binary adder by any
               separate code are developed. We demonstrate the existence of
               separate checking codes for addition modulo $2^n$ (n >= 4)
               and modulo $2^n$-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 intial 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, we
               examine a modulo $2^n$ adder where the carry out of the high
               position is also presented to a checker.
       NOTES:: [Adminitrivia V1/Prg/19941201]
         END:: STAN//CSL-TR-72-35