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On the equivalence of linear codes
Applicable Algebra in Engineering, Communication and Computing, 2011The authors consider the problem of equivalence of linear codes, i.e., when they differ by a linear isometry of the Hamming space. In that case, the linear isometry is exactly a monomial transformation. Certain equivalent conditions are derived for this notion of equivalence, based upon properties of the relative codes obtained from the relative ...
Zihui Liu, Zhimin Sun
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IEEE Transactions on Information Theory, 2003
Summary: Consider a communication network in which certain source nodes multicast information to other nodes on the network in the multihop fashion where every node can pass on any of its received data to others. We are interested in how fast each node can receive the complete information, or equivalently, what the information rate arriving at each ...
Shuo-Yen Robert Li +2 more
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Summary: Consider a communication network in which certain source nodes multicast information to other nodes on the network in the multihop fashion where every node can pass on any of its received data to others. We are interested in how fast each node can receive the complete information, or equivalently, what the information rate arriving at each ...
Shuo-Yen Robert Li +2 more
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On the maximality of linear codes
Designs, Codes and Cryptography, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
T. L. Alderson, András Gács
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Problems of Information Transmission, 2017
One of the most famous equalities in coding theory is the McWilliams equality giving a relation between the spectrum \(\{a_0,\ldots,a_n\}\) of a vector space \(V\) and \(\{b_0,\ldots,b_n\}\) of its orthogonal subspace \(V^\ast.\) In this work, V. K. Leont'ev presents a MacWilliams-type equality by analyzing the behavior of the sequence \(\left\{a_s ...
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One of the most famous equalities in coding theory is the McWilliams equality giving a relation between the spectrum \(\{a_0,\ldots,a_n\}\) of a vector space \(V\) and \(\{b_0,\ldots,b_n\}\) of its orthogonal subspace \(V^\ast.\) In this work, V. K. Leont'ev presents a MacWilliams-type equality by analyzing the behavior of the sequence \(\left\{a_s ...
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Linear codes and the mitochondrial genetic code
Biosystems, 2019The origin of the genetic code can certainly be regarded as one of the most challenging problems in the theory of molecular evolution. Thus the known variants of the genetic code and a possible common ancestry of them haven been studied extensively in the literature. Gonzalez et al.
Elena Fimmel, Lutz Strüngmann
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IEEE Transactions on Information Theory, 1998
Summary: Slepian (1960) introduced a structure theory for linear, binary codes and proved that every such code was uniquely the sum of indecomposable codes. He had hoped to produce a canonical form for the generator matrix of an indecomposable code so that he might read off the properties of the code from such a matrix, but such a program proved ...
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Summary: Slepian (1960) introduced a structure theory for linear, binary codes and proved that every such code was uniquely the sum of indecomposable codes. He had hoped to produce a canonical form for the generator matrix of an indecomposable code so that he might read off the properties of the code from such a matrix, but such a program proved ...
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2018 IEEE International Symposium on Information Theory (ISIT), 2018
In this paper, we construct a new family of codes-linearized Goppa codes embedded with Hamming and rank metric, and determine their parameters. In addition, we give a decoding method with respect to Hamming metric.
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In this paper, we construct a new family of codes-linearized Goppa codes embedded with Hamming and rank metric, and determine their parameters. In addition, we give a decoding method with respect to Hamming metric.
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Linear Codes and Their Coordinate Ordering
Designs, Codes and Cryptography, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sylvia B. Encheva, Gérard D. Cohen
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A Propagation Rule for Linear Codes
Applicable Algebra in Engineering, Communication and Computing, 2000By a propagation rule it is meant a procedure or a theorem leading to new codes from old ones. The authors introduce a propagation rule for linear codes by considering certain function field extensions. The parameters (length, dimension, distance) of the new code are related to the parameters of the old code and also to three chosen integers.
Harald Niederreiter, Chaoping Xing
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Linear Codes and Character Sums
COMBINATORICA, 2002\textit{G. Kalai} and \textit{N. Linial} [IEEE Trans. Inf. Theory 41, 1467-1472 (1995; Zbl 0831.94019)] conjectured that the size of the code with the distribution of distances near the minimal distance is exponentially small. The authors estimate the fraction of non-zero vectors of minimal weights in an \(r\cdot n\)-dimensional subspace of \(\mathbb{Z}
Nathan Linial, Alex Samorodnitsky
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