The Weight Enumerators for Several Clauses of Subcodes of the 2nd Order Binary Reed-Muller Codes

In this paper explicit formulas for the weight enumerators for several classes of subcodes of the 2nd-order binary Reed-Muller codes are derived. A large set of the codes are shown to have the same weight enumerators. The classes of codes studied in this paper contain the (0, 2)th-order Euclidean Geometry codes and the codes studied by Berlekamp as subclasses.