Error detecting capabilities of the shortened Hamming codes adopted for error detection in IEEE Standard 802.3

The error-detecting capabilities of the shortened Hamming codes adopted for error detection in IEEE Standard 802.3 are investigated. These codes are also used for error detection in the data link layer of the Ethernet, a local area network. The weight distributions for various code lengths are calculated to obtain the probability of undetectable error and that of detectable error for a binary symmetric channel with bit-error rate between 0.00001 and 1/2.