Abstract Algebra Theory and Applications - Computer Science ...

54 CHAPTER 2 GROUPS0 50000 30042 6Figure 2.3. A UPC code2. It is often useful to use an inner product notation for this type of errordetection scheme; hence, we will use the notion(d 1 , d 2 , . . . , d k ) · (w 1 , w 2 , . . . , w k ) ≡ 0 (mod n)to meand 1 w 1 + d 2 w 2 + · · · + d k w k ≡ 0(mod n).Suppose that (d 1 , d 2 , . . . , d k )·(w 1 , w 2 , . . . , w k ) ≡ 0 (mod n) is an error detectionscheme for the k-digit identification number d 1 d 2 · · · d k , where 0 ≤ d i