311 research outputs found
A class of narrow-sense BCH codes over of length
BCH codes with efficient encoding and decoding algorithms have many
applications in communications, cryptography and combinatorics design. This
paper studies a class of linear codes of length over
with special trace representation, where is an odd prime
power. With the help of the inner distributions of some subsets of association
schemes from bilinear forms associated with quadratic forms, we determine the
weight enumerators of these codes. From determining some cyclotomic coset
leaders of cyclotomic cosets modulo , we prove
that narrow-sense BCH codes of length with designed distance
have the corresponding trace representation, and have the
minimal distance and the Bose distance , where
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm
Advances in Syndrome Coding based on Stochastic and Deterministic Matrices for Steganography
Steganographie ist die Kunst der vertraulichen Kommunikation. Anders als in der Kryptographie, wo der Austausch vertraulicher Daten für Dritte offensichtlich ist, werden die vertraulichen Daten in einem steganographischen System in andere, unauffällige Coverdaten (z.B. Bilder) eingebettet und so an den Empfänger übertragen.
Ziel eines steganographischen Algorithmus ist es, die Coverdaten nur geringfügig zu ändern, um deren statistische Merkmale zu erhalten, und möglichst in unauffälligen Teilen des Covers einzubetten. Um dieses Ziel zu erreichen, werden verschiedene Ansätze der so genannten minimum-embedding-impact Steganographie basierend auf Syndromkodierung vorgestellt. Es wird dabei zwischen Ansätzen basierend auf stochastischen und auf deterministischen Matrizen unterschieden. Anschließend werden die Algorithmen bewertet, um Vorteile der Anwendung von Syndromkodierung herauszustellen
Efficient Algorithms for Constructing Minimum-Weight Codewords in Some Extended Binary BCH Codes
We present algorithms for specifying the support of minimum-weight
words of extended binary BCH codes of length and designed distance
for some values of , where may
grow to infinity. The support is specified as the sum of two sets: a set of
elements, and a subspace of dimension , specified by
a basis.
In some detail, for designed distance , we have a deterministic
algorithm for even , and a probabilistic algorithm with success
probability for odd . For designed distance ,
we have a probabilistic algorithm with success probability for even . Finally, for designed distance , we have a deterministic algorithm for divisible by . We also
present a construction via Gold functions when .
Our construction builds on results of Kasami and Lin (IEEE T-IT, 1972), who
proved that for extended binary BCH codes of designed distance , the
minimum distance equals the designed distance. Their proof makes use of a
non-constructive result of Berlekamp (Inform. Contrl., 1970), and a
constructive ``down-conversion theorem'' that converts some words in BCH codes
to lower-weight words in BCH codes of lower designed distance. Our main
contribution is in replacing the non-constructive argument of Berlekamp by a
low-complexity algorithm.
In one aspect, we extends the results of Grigorescu and Kaufman (IEEE T-IT,
2012), who presented explicit minimum-weight words for designed distance
(and hence also for designed distance , by a well-known
``up-conversion theorem''), as we cover more cases of the minimum distance.
However, the minimum-weight words we construct are not affine generators for
designed distance
- …