Error Detection inDigital Devices andComputer Programs with theAidofLinear Recurrent Equations OverFinite Commutative Groups
Mark G. Karpovsky · 1977
A methodisproposed forerrordetection indigital devices andcomputer programs calculating thevalues offunctions f(x), wherexe GandGisafinite commutative group. Forthecase ofnetwork implementation ofthemethod, errors arecatastrophic structural failures; forthecaseofprogramimplementation, they areerrors inthetextoftheprogram. Themethodisbased onfinding, given thefunction, alinear re- current equation overGwithcoefficients 0or1,ofwhichfisa solution. Theverification whether this isindeed thecaseconstitutes anerrordetection method. Implementation ofthemethodrequires onlytheoperations of summation, delay, andthegroupoperation inG. Theequation whosesolution isthegiven function fwill besought using methods ofabstract harmonic analysis onthegroupG. IndexTerms-Error detection for, digital devices andcomputer programs, errordetection tests fordigital devices, characters of commutative groups, Fourier transform overfinite commutative groups, spectral andautocorrelation functions overfinite com- mutative groups, fast Hadamard-Walsh transform.