CONSIDERATIONS ON CORRELATIONS IN SHIFT-REGISTER PSEUDORANDOM NUMBER GENERATORS AND THEIR REMOVAL

We present a simple calculation quantitatively explaining the triplet correlations in the popular shift-register random number generator ''R 250'', which were recently observed numerically by Schmid and Wilding, and are known from general analysis of this type of generator. Starti ng from these considerations, we discuss various methods to remove the se correlations by combining different shift-register generators. We i mplement and test a particularly simple and fast version, based on an XOR combination of two independent shift-register generators with diff erent time lags. The results indicate that this generator has much bet ter statistical properties than R250, while being only a factor of two slower. This is consistent with previous analytical considerations an d successful applications of this type of generator. The known nine-po int correlations still present in the generator are quantitatively und erstood by our simple arguments.