RESEARCH IN MATHEMATICS AND COMPUTER SCIENCE: CALCULATION OF THE PROBABILITY OF UNDETECTED ERROR FOR CERTAIN ERROR DETECTION CODES

BINARY CYCLIC REDUNDANCY CHECK CODES, KNOWN AS CRC CODES, ARE UTILIZED AS MESSAGE ERROR DETECTION CODES IN APPLICATIONS REQUIRING VERY HIGH CONFIDENCE THAT A MESSAGE IS RECEIVED ERROR FREE. OFTEN, IT IS ASSUMED THAT THE PROBABILITY OF UNDETECTED ERROR FOR THESE CODES IS UPPER BOUNDED BY 2(-R), WHERE R IS THE NUMBER OF REDUNDANT (PARITY) BITS. THIS UPPER BOUND IS NOT CORRECT FOR MANY CODES, HOWEVER, ESPECIALLY SHORTENED CYCLIC CODES. WE HAVE FOUND A NEW METHOD FOR DETERMINING AN EXACT EVALUATION OF THE PROBABILITY OF UNDETECTED ERROR FOR THE MOST COMMONLY UTILIZED CODES. WE PROPOSE TO INVESTIGATE HOW THIS METHOD CAN BE UTILIZED TO PRODUCE THE VERY BEST MESSAGE ERROR DETECTION CODES.