On Constructions of Reed-Muller Subcodes

In this letter, subcodes constructed from Reed-Muller codes by removal of generator matrix rows are considered. A new greedy algorithm based on the overlap of generator matrix rows is developed. To select the best subcode generated by the greedy algorithm, the number of minimum weight code words is determined. Computer simulations confirm that the greedy algorithm outperforms the three other construction methods, generating the best codes among all presented subcodes.