The realization and application of parallel linear feedback shift registers

Two methods for serial-to-parallel transformation of linear feedback shift registers are briefly discussed. A third method for transformation is rigorously developed using a next-state and output equation representation of the linear feedback shift register. An algorithm is developed for simplifying the parallel machine resulting from serial-to-parallel transformation, where simplification is defined as reduction in the required number of modulo 2 adders. A computer program incorporating serial-to-parallel transformation and the simplification algorithm is provided --Abstract, page ii

Note on Marsaglia's Xorshift Random Number Generators

Marsaglia (2003) has described a class of Xorshift random number generators (RNGs) with periods 2n - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using "exclusive or" (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n

On cross joining de Bruijn sequences

We explain the origins of Boolean feedback functions of nonlinear feedback shift registers (NLFSRs) of fixed order n generating de Bruijn binary sequences. They all come into existence by cross joining operations starting from one maximum period feedback shift register, e.g., a linear one which always exists for any order n. The result obtained yields some constructions of NLFSRs generating maximum period $2^n-1$ binary sequences