Spinor field realizations of the non-critical $W_{2,4}$ string based on   the linear $W_{1,2,4}$ algebra
  In this paper, we investigate the spinor field realizations of the $W_{2,4}$ algebra, making use of the fact that the $W_{2,4}$ algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical $W_{2,4}$ string were built with these realizations. 
Li-Jie Zhang, Yu-Xiao Liu