  A class of xorshift random number generators (RNGs) are introduced by
Marsaglia. We have proposed an algorithm which constructs a full period
xorshift RNG from a given primitive polynomial. It is shown there is a weakness
present in those RNGs and is suggested its improvement. A separate algorithm is
also proposed which returns a full period xorshift generator with desired
number of xorshift operations.%We also introduce the notion of tweaked
primitive multiple-recursive matrix method with improved linear complexity.
