# Xorshift random number generators from primitive polynomials

## TL;DR

This paper introduces algorithms to construct full period xorshift RNGs from primitive polynomials, identifies weaknesses in existing RNGs, and proposes improvements along with a new recursive matrix method for better linear complexity.

## Contribution

It presents novel algorithms for creating full period xorshift RNGs from primitive polynomials and introduces a tweaked recursive matrix method with enhanced linear complexity.

## Key findings

- Identified weaknesses in existing xorshift RNGs.
- Developed algorithms for constructing full period RNGs.
- Proposed an improved recursive matrix method.

## Abstract

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.