1. A method for state transition matrix-based linear feedback shift register computations, said method comprising: computing a transition matrix associated with a linear feedback shift register, said transition matrix comprising a k-step transition matrix based on a single step state transition matrix; computing an output matrix associated with said linear feedback shift register defined such that an input bit is a linear function of a previous state and external input bits and comprises more than one feedback as input; combining said transition matrix with said output matrix; reducing a size of said transition matrix and said output matrix following combining said transition matrix with said output matrix; and configuring said transition matrix to comprise said single step state transition matrix wherein a size of said k-step transition matrix is increased from L*(L+k) to k*(L+k), but an output generating matrix is reduced from k*(L+k) to zero, thereby providing an improved speedup capability for calculating a next state and/or an output of said linear feedback shift register.