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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Applicable Algebra i...arrow_drop_down
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Applicable Algebra in Engineering Communication and Computing
Article . 1998 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Data sources: zbMATH Open
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Article . 1998
Data sources: DBLP
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On the Concatenated Structure of a Linear Code

On the concatenated structure of a linear code
Authors: Nicolas Sendrier;

On the Concatenated Structure of a Linear Code

Abstract

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 replacing the elements of \(F_{q^{k_B}}\) by codewords of \(B\) according to a map \(\Theta\) from \((F_{q^{k_B}})^{n_E}\) to \(B^{n_E}\). The problem considered here is to determine a concatenated structure of a linear code, given its generating matrix, i.e. determine the inner and outer codes, if they exist. In section 3 of the paper, three steps are given for recovering the concatenated structure of the code: (i) The support of the code is partitioned in a number of blocks, called inner blocks and the restriction of \({\mathcal C}\) to any one of these blocks is equal to the inner code. The inner blocks and a generating matrix of the inner code are recovered by using the properties of the dual of a concatenated code. (ii) The inner blocks are reordered by finding a permutation between two small equivalent binary codes. (iii) A particular generating matrix is found and used to recover a generating matrix of the outer code. Section 4 of the paper describes an implementation of the entire procedure and gives comments on its algorithmic complexity.

Keywords

Cryptography, Algebraic coding theory; cryptography (number-theoretic aspects), outer codes, inner codes, linear codes over finite fields, concatenated codes, implementation, Linear codes (general theory)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
34
Top 10%
Top 10%
Average
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