Results 131 to 140 of about 516,863 (164)

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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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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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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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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Computing Linear Codes and Unitals

Designs, Codes and Cryptography, 1998
A unital on \(q^3+1\) points is a 2-\((q^3+1,q+1,1)\) design. The Ree unital \(R(q)\) on \(q^3+1\) points for \(q=3^{2m+1}\), \(m\geq 0\) is a design invariant under the Ree group. In 1981, Andries Brouwer constructed 138 nonisomorphic 2-\((28,42,1)\) designs and made the conjecture that the Ree unital \(R(3)\) is characterized by the fact that its ...
David B. Jaffe, Vladimir D. Tonchev
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Linear codes and weights [PDF]

Australas. J Comb., 1993
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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Linear Codes and Their Coordinate Ordering

Designs, Codes and Cryptography, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sylvia B. Encheva, Gérard D. Cohen
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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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Extendability of Ternary Linear Codes

Designs, Codes and Cryptography, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Concatenated Structure of a Linear Code

Applicable Algebra in Engineering, Communication and Computing, 1998
Let \(F_q\) be a finite field with \(q\) elements and denote by \(C(n,k,d)\) a linear code of length \(n\) over \(F_q\) of dimension \(k\) and minimum distance \(d\). Define \(B(n_B,k_B,d_B)\) over \(F_q\) to be an inner code, \(E(n_E,k_E,d_E)\) over \(F_{q^{k_B}}\) to be an outer code and \({\mathcal C}\) to be the concatenateed code, obtained by ...
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