Minimal codewords in Reed–Muller codes
نویسندگان
چکیده
منابع مشابه
Minimal codewords in Reed-Muller codes
Minimal codewords were introduced by Massey [8] for cryptographical purposes. They are used in particular secret sharing schemes, to model the access structures. We study minimal codewords of weight smaller than 3·2m−r in binary Reed-Muller codes RM(r, m) and translate our problem into a geometrical one, using a classification result of Kasami, Tokura, and Azumi [5, 6] on Boolean functions. In ...
متن کاملBounds on Minimal Codewords in Linear Codes
The notion of minimal codewords in linear codes was introduced recently by Massey. In this paper two weight bounds on minimal code-words are proved; an upper bound above which no codewords are minimal and a lower bound below which all codewords are minimal. It is shown for Hamming codes that every weight class between the two bounds contains at least one minimal codeword and at least one non-mi...
متن کاملBinary Cyclic Codes and Minimal Codewords
Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all ...
متن کاملOn the Non-minimal Codewords in Binary Reed-Muller Codes
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.
متن کاملThe maximum number of minimal codewords in long codes
Upper bounds on the maximum number of minimal codewords in a binary code follow from the theory of matroids. Random coding provide lower bounds. In this paper we compare these bounds with analogous bounds for the cycle code of graphs. This problem (in the graphic case) was considered in 1981 by Entringer and Slater who asked if a connected graph with p vertices and q edges can have only slightl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2009
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-009-9323-x