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The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes. (English) Zbl 0217.58802
Summary: 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 E. R. Berlekamp [Inf. Control 17, 485–500 (1970; Zbl 0211.51304)] as subclasses.

MSC:
94B15 Cyclic codes
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