منابع مشابه
The Witt designs, Golay codes and Mathieu groups
Let V be a vector space over Fq with fixed basis e1, ..., en. A code C is a subset of V . A linear code is a subspace of V . The vector with all coordinates equal to zero (resp. one) will be denoted by 0 (resp. 1). The Hamming distance dH(u, v) between two vectors u, v ∈ V is the number of coordinates where they differ: when u = ∑ uiei, v = ∑ viei then dH(u, v) = |{i | ui 6= vi}|. The weight of...
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We discuss a specific type of error-control coding using Golay codes. First we introduce the basics of coding. Then we discuss the Golay code in binary form, extended binary form, and ternary form.
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In any connected, undirected graph G = (V, E), the distance d(x, y) between two vertices x and y of G is the minimum number of edges in a path linking x to y in G. A sphere in G is a set of the form Sr (x) = {y ∈ V : d(x, y) = r}, where x is a vertex and r is a nonnegative integer called the radius of the sphere. We first address in this paper the following question: What is the minimum number ...
متن کاملDecoding the Mathieu Group
The sporadic Mathieu group M12 can be viewed as an errorcorrecting code, where the codewords are the group’s elements written as permutations in list form, and with the usual Hamming distance. We investigate the properties of this group as a code, in particular determining completely the probabilities of successful and ambiguous decoding of words with more than 3 errors (which is the number tha...
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Golay codewords are useful for transmission schemes such as OFDM, and [MacWilliams/Sloane] demonstrated that these codewords are bent functions contained in second order Reed-Muller codes. This paper investigates the intersection between these codes and Kerdock-like codes.
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2002
ISSN: 0304-9914
DOI: 10.4134/jkms.2002.39.2.289