Algebraic structure of the minimal support codewords set of some linear codes
نویسندگان
چکیده
منابع مشابه
Algebraic structure of the minimal support codewords set of some linear codes
It has been widely known that complete decoding for binary linear codes can be regarded as an linear integer programming problem with binary arithmetic conditions. Conti and Traverso [8] have proposed an efficient algorithm which uses Gröbner bases to solve integer programming with ordinary integer arithmetic conditions. Ikegami and Kaji [11] extended the Conti-Traverso algorithm to solve integ...
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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...
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In order to obtain the set of codewords of minimal support of codes defined over Zq we must compute a Graver basis of the ideal associated to such codes, see [9]. The main aim of this article is to reduce the complexity of the previous algorithm taking advantage of the powerful decomposition theory for linear codes provided by the decomposition theory of representable matroids over finite field...
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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 ...
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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 ...
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ژورنال
عنوان ژورنال: Advances in Mathematics of Communications
سال: 2011
ISSN: 1930-5346
DOI: 10.3934/amc.2011.5.233