Blind recognition of BCH code based on Galois field fourier transform

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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Blind Recognition of Reed-Solomon Codes Based on Histogram Statistic of Galois Field Spectra

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.791-793.2088 ◽

2013 ◽

Vol 791-793 ◽

pp. 2088-2091

Author(s):

Hui Xie ◽

Feng Hua Wang ◽

Zhi Tao Huang

Keyword(s):

Reverse Engineering ◽

Error Rate ◽

Communication System ◽

Spectral Characteristics ◽

Galois Field ◽

Probability Of Detection ◽

Noisy Environment ◽

Engineering Communication ◽

Rs Code ◽

Blind Recognition

We focus on the recognition of RS code in a reverse-engineering communication system, and an algorithm based on spectral statistic is proposed, which makes use of the spectral characteristics of RS code. When there are some codes with errors in the observations, the spectral histogram statistic is computed, which can improve the probability of detection in the noisy environment. Experimental results are given to illustrate the performances of the method which can get a 90% probability of detection of (255, 223) RS code in the presence of 0.5% code error rate.

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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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