On the maximum value of aliasing probabilities for single input signature registers

The aliasing error performance of a signature register is measured by the maximum values of the aliasing error probabilities for certain ranges of the bit-error rate (and those of the test length). Based on these measures, we evaluate the performances of all the single input signature registers whose feedback polynomials are primitive polynomials of degree 16 and generator polynomials of the double-error-correcting BCH codes of the same degree. When the degree of the feedback polynomial is large, say 32, it is computationally hard to obtain the exact aliasing probability. But we observe that the numbers of codewords with large weights in the corresponding code dominate the maximum value of the aliasing probabilities. By computing the numbers of codewords of large weights, we find primitive polynomials of degree 32 whose maximum value of the aliasing probabilities is very large for some test lengths. The error performance of an LFSR with any BCH polynomial of degree m for the test length 2^m/2-2 is shown to be very good by deriving the formula for the weight distribution of the corresponding code