منابع مشابه
On Linear Ordered Codes
We consider linear codes in the metric space with the Niederreiter-Rosenbloom-Tsfasman (NRT) metric, calling them linear ordered codes. In the first part of the paper we examine a linear-algebraic perspective of linear ordered codes, focusing on the distribution of “shapes” of codevectors. We define a multivariate Tutte polynomial of the linear code and prove a duality relation for the Tutte po...
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چکیده ندارد.
15 صفحه اولPerfect Codes on Some Ordered Sets
Using the concept of codes on ordered sets introduced by Brualdi, Graves and Lawrence, we consider perfect codes on the ordinal sum of two ordered sets, the standard ordered sets and the disjoint sum of two chains. In the classical coding theory all perfect codes are completely described in terms of parameters (cf. [2, 3]). They are mathematically interesting structures. Brualdi et al. [1] rece...
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Linear code with complementary dual(LCD) are those codes which meet their duals trivially. In this paper we will give rather alternative proof of Massey’s theorem[8], which is one of the most important characterization of LCD codes. Let LCD[n, k]3 denote the maximum of possible values of d among [n, k, d] ternary codes. We will give bound on LCD[n, k]3. We will also discuss the cases when this ...
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This paper studies and classifies linear transformations that connect Hamming distances of codes. These include irreducible linear transformations and their concatenations. Their effect on the Hamming weights of codewords is also studied. Both linear and non-linear codes over fields are considered. We construct a family of pure binary quantum codes using these transformations. It is shown that ...
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ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2015
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2015-15-4-679-702