Analysis and Generation of Test Sequences Based on Hamming Code and its Modifications

The probability of error masking (non-detection) in an output sequence of a device-under-test (DUT) is often used as a measure of the efficiency and validity of compact testing (i.e., testing where long test response sequences are compressed (compacted) into their short representations - so-called signatures, which then compared with reference values corresponding to the fault-free operation of DUT). The paper deals with the distribution of probabilities of the error masking by the method of compact testing based on the Hamming code (widely known as a signature analysis) and by two other methods having characteristics of certain modifications of the Hamming code. The paper presents the derivation of the analytical expressions for the number of code words of an arbitrary weight in the codes under discussion. Such a number indicates how many different long sequences could be compacted into the same short signature word thus leading to error masking. The paper then evaluates the non-one max and non-zero min boundaries for the error masking. In addition an algorithm for generation of all the code words of a given weight for the extended Hamming code (the code with the best error detection properties out of the analysed three code types) is proposed