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 $\text{gf}(q)$ 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.