Shortened Cyclic Codes for Correcting and Detecting Burst Errors

New optimum binary shortened cyclic codes with redundancy r = 32 and burst-error correction capability b are presented. The codes are found by performing an exhaustive computer search using the Kasami algorithm, and their performance is compared with analytical bounds by Reiger, Abramson and Campopiano. The true burst-error correction capability of the [2112, 2080] shortened Fire code selected for 10 Gb/s Ethernet is determined to be b = 11 and [2112, 2080] shortened cyclic codes with higher burst-error correction capability b = 13 are given. The double burst-error detection properties of three cyclic redundancy check codes used in standards are compared.