Another Generalization of the Reed-Muller Codes
  The punctured binary Reed-Muller code is cyclic and was generalized into the punctured generalized Reed-Muller code over $\gf(q)$ in the literature. The major objective of this paper is to present another generalization of the punctured binary Reed-Muller code. Another objective is to construct a family of reversible cyclic codes that are related to the newly generalized Reed-Muller codes. 
Cunsheng Ding, Chunlei Li, and Yongbo Xia
cs.IT math.IT