This paper presents parallel signature design techniques that guarante
e the aliasing probability to be less than 2/L, where L is the test le
ngth. Using y signature samples, a parallel signature analysis design
is proposed that guarantees the aliasing probability to be less than (
y/L)(y/2). Inaccuracies and incompleteness in previously published bou
nds on the aliasing probability are discussed. Simple bounds on the al
iasing probability are derived for parallel signature designs using pr
imitive polynomials.