On the Non-minimal Codewords in Binary Reed-Muller Codes
نویسندگان
چکیده
First, we compute the number of non-minimal codewords of weight 2dmin in the binary Reed-Muller code RM(r,m). Second, we prove that all codewords of weight greater than 2m − 2m−r+1 in binary RM(r,m), are non-minimal.
منابع مشابه
On the non-minimality of the largest weight codewords in the binary Reed-Muller codes
The study of minimal codewords in linear codes was motivated by Massey who described how minimal codewords of a linear code define access structures for secret sharing schemes. As a consequence of his article, Borissov, Manev, and Nikova initiated the study of minimal codewords in the binary Reed-Muller codes. They counted the number of non-minimal codewords of weight 2d in the binary Reed-Mull...
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 128 شماره
صفحات -
تاریخ انتشار 2003