135 research outputs found
Wet paper codes and the dual distance in steganography
In 1998 Crandall introduced a method based on coding theory to secretly embed
a message in a digital support such as an image. Later Fridrich et al. improved
this method to minimize the distortion introduced by the embedding; a process
called wet paper. However, as previously emphasized in the literature, this
method can fail during the embedding step. Here we find sufficient and
necessary conditions to guarantee a successful embedding by studying the dual
distance of a linear code. Since these results are essentially of combinatorial
nature, they can be generalized to systematic codes, a large family containing
all linear codes. We also compute the exact number of solutions and point out
the relationship between wet paper codes and orthogonal arrays
Improving success probability and embedding efficiency in code based steganography
For stegoschemes arising from error correcting codes, embedding depends on a
decoding map for the corresponding code. As decoding maps are usually not
complete, embedding can fail. We propose a method to ensure or increase the
probability of embedding success for these stegoschemes. This method is based
on puncturing codes. We show how the use of punctured codes may also increase
the embedding efficiency of the obtained stegoschemes
An Introduction to Algebraic Geometry codes
We present an introduction to the theory of algebraic geometry codes.
Starting from evaluation codes and codes from order and weight functions,
special attention is given to one-point codes and, in particular, to the family
of Castle codes
Locally recoverable J-affine variety codes
A locally recoverable (LRC) code is a code over a finite eld Fq such that
any erased coordinate of a codeword can be recovered from a small number of other
coordinates in that codeword. We construct LRC codes correcting more than one erasure,
which are sub eld-subcodes of some J-affine variety codes. For these LRC codes, we
compute localities (r; )) that determine the minimum size of a set R of positions so that
any - 1 erasures in R can be recovered from the remaining r coordinates in this set.
We also show that some of these LRC codes with lengths n >> q are ( - 1)-optimal
Locally recoverable codes from rational maps
Producción CientíficaWe give a method to construct Locally Recoverable Error-Correcting codes.
This method is based on the use of rational maps between affine spaces. The recovery of
erasures is carried out by Lagrangian interpolation in general and simply by one addition
in some good cases.Ministerio de Economía, Industria y Competitividad ( grant MTM2015-65764-C3-1-P)Consejo Nacional de Desarrollo Científico y Tecnológico- Brasil (grants 159852/2014-5 / 201584/2015-8
Locally recoverable codes from the matrix-product construction
Matrix-product constructions giving rise to locally recoverable codes are
considered, both the classical and localities. We study the
recovery advantages offered by the constituent codes and also by the defining
matrices of the matrix product codes. Finally, we extend these methods to a
particular variation of matrix-product codes and quasi-cyclic codes.
Singleton-optimal locally recoverable codes and almost Singleton-optimal codes,
with length larger than the finite field size, are obtained, some of them with
superlinear length
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