The Mersenne Twister algorithm is based on a matrix linear recurrence over a finite binary field . The algorithm is a twisted generalised feedback shift register (twisted GFSR, or TGFSR) of rational normal form (TGFSR(R)), with state bit reflection and tempering. The basic idea is to define a series through a simple recurrence relation, and then output numbers of the form , where T is an invertible -matrix called a tempering matrix.
The Mersenne Twister algorithm is based on a matrix linear recurrence over a finite binary field  The algorithm is a twisted generalised feedback shift register (twisted GFSR, or TGFSR) of rational normal form (TGFSR(R)) with state bit reflection and tempering, The basic idea is to define a series through a simple recurrence relation, and then output numbers of the form  where T is an inve.rtible -matrix called a ,tempering matrix.