A study on linear pseudorandom number generators with long period

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We studied pseudorandom number generators based on linear recurrences over finite fields. Pseudorandom numbers are indispensable tools for Monte Carlo simulations. Linear pseudorandom number generators are often used in the simulations. In this research, we studied properties of linear pseudorandom number generators in the weight distribution tests. Relationship between the form of the recurrence of generators and their initial states are studied. We analyzed also relationship between the form of the recurrence and their outputs in the weight distribution tests. We constructed pseudorandom number generators with maximally equidistribution property.