Results 321 to 330 of about 9,454,079 (375)

Linear network coding

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, Raymond W. Yeung, Ning Cai 0001   +2 more
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On Spectra of Linear Codes

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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A (48, 31, 8) linear code (Corresp.)

IEEE Transactions on Information Theory, 1973
V. V. Rao, S. Reddy
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Hardness of approximating the minimum distance of a linear code

40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039), 1999
We show that the minimum distance of a linear code (or equivalently, the weight of the lightest codeword) is not approximable to within any constant factor in random polynomial time (RP), unless NP equals RP.
I. Dumer, Daniele Micciancio, M. Sudan
semanticscholar   +1 more source

The category of linear codes

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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Linearized Goppa Codes

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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Linear codes and weights [PDF]

Australas. J Comb., 2020
We give an algebraic characterization of weight functions on linear codes, i.e. vector spaces of \(n\)-tuples over a finite field. Specifically, given a function from a finite vector space \(V\) to the nonnegative integers, we determine precisely when \(V\) can be replaced (isomorphically) by a space of \(n\)-tuples so that the given function becomes ...
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A Propagation Rule for Linear Codes

Applicable Algebra in Engineering, Communication and Computing, 2000
By 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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Extendability of Ternary Linear Codes

Designs, Codes and Cryptography, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Extension Theorem for Linear Codes

Designs, Codes and Cryptography, 1999
The author gives a simple sufficient condition for the existence of an extension of an \([n,k,d]_q\) code (with \((d,q)=1\)) to an \([n+1,k,d+1]_q\) code: if the weights of the code are all congruent to \(0\) or \(d\) modulo \(q\) then the code can be extended and the weights of the new code are all congruent to \(0\) or \(d+1\) modulo \(q\). The proof
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