Blind Detection Scheme for the Size of Galois Field of BCH Code

The entanglement-assisted (EA) formalism generalizes the standard stabilizer formalism. All quaternary linear codes can be transformed into entanglement-assisted quantum error correcting codes (EAQECCs) under this formalism. In this work, we discuss construction of EAQECCs from Hermitian non-dual containing primitive Bose–Chaudhuri–Hocquenghem (BCH) codes over the Galois field GF(4). By a careful analysis of the cyclotomic cosets contained in the defining set of a given BCH code, we can determine the optimal number of ebits that needed for constructing EAQECC from this BCH code, rather than calculate the optimal number of ebits from its parity check matrix, and derive a formula for the dimension of this BCH code. These results make it possible to specify parameters of the obtained EAQECCs in terms of the design parameters of BCH codes.

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PROPERTIES OF GROUPS G OF DOUBLE ERRORS AND ITS INVARIANTS IN BCH CODES

«System analysis and applied information science» ◽

10.21122/2309-4923-2018-2-40-46 ◽

2018 ◽

pp. 40-46

Author(s):

V. A. Lipnitskij ◽

A. V. Serada

Keyword(s):

Irreducible Polynomial ◽

Galois Field ◽

Bch Codes ◽

Bch Code ◽

Polynomial Invariant ◽

Polynomial Invariants ◽

The Core ◽

Complex Process ◽

Scope Of Application ◽

Complete Set

The goal of the work is the further extending the scope of application of code automorthism in methods and algorithms of error correction by these codes. The effectiveness of such approach was demonstrated by norm of syndrome theory that was developed by Belarusian school of noiseless coding at the turn of the XX and XXI century. The group Г of the cyclical shift of vector component lies at the core of the theory. Under its action The error vectors are divided into disjoint Г-orbits with definite spectrum of syndromes. This allowed to introduce norms of syndrome of a family of BCH codes that are invariant over action of group Г. Norms of syndrome are unique characteristic of error orbit Г of any decoding set, hence it is the basis of permutation norm methods of error decoding. Looking over the Г-orbits of errors not the errors these methods are faster than classic syndrome methods of error decoding, are avoided from the complex process of solving the algebraic equation in Galois field, are simply implemented.A detailed theory for automorphism group G of BCH codes obtained by adding cyclotomic substitution to the group Г develops in the article. The authors held a detailed study of structure of G-orbit of errors as union of orbits Г of error vectors; one-to-one mapping of this structure on the norm structure of group Г. These norms being interconnected by Frobenius automorphism in the Galois field – field of BCH code constitute the complete set of roots of the only irreducible polynomial. It is a polynomial invariant of its orbit G. The main focus of the work is on the description of properties and specific features of groups G of double errors and its polynomial invariants.

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Robust Watermarking of Polygonal Meshes Based on Vertex Norms Variance Distortion

Journal of Global Information Management ◽

10.4018/jgim.2017100104 ◽

2017 ◽

Vol 25 (4) ◽

pp. 46-60 ◽

Cited By ~ 3

Author(s):

Yesmine Ben Amar ◽

Imen Trabelsi ◽

Nilanjan Dey ◽

Fuqian Shi ◽

Suresh Chandra Satapathy ◽

...

Keyword(s):

Copyright Protection ◽

Data Transfer ◽

Three Dimensional ◽

Blind Detection ◽

Robust Watermarking ◽

Polygonal Meshes ◽

Detection Scheme ◽

Media Type ◽

Digital Contents

The three-dimensional (3D) mesh is moderately novel media type that realizes a rising success in various applications through data transfer via the Internet, which requires security approaches. Technological copyright protection of digital contents has become a challenging task in the current digital epoch. In this work, a robust watermarking algorithm of polygonal meshes for copyright protection purposes is proposed. The watermark insertion was achieved by quantization of the vertex norms variance in order to insert the watermark bits. In addition, this method is based on a blind detection scheme, so the watermark can be extracted without referring to the original mesh. The experimental results established the quality of the watermarked object as well as the inserted watermark robustness against various types of attacks, which were evaluated to prove the validity of the proposed algorithm. The results proved the proposed method efficiency in terms of robustness and imperceptibility against several signal processing distortions. A comparison with other reported method with similar purposes is also provided. The comparison depicted the outstanding robustness of the proposed method compared to the other reported method.

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