About the Ultimate Efficiency of Interference Binary Codes

Mapping Intimacies ◽

10.20944/preprints202110.0315.v1 ◽

2021 ◽

Author(s):

Artem Sergeevich Adzhemov ◽

Nicolay Yurievich Albov

Keyword(s):

Communication Channel ◽

Linear Codes ◽

Binary Codes ◽

Digital Representation ◽

Ultimate Efficiency

The digital representation of various signals allows, at the subsequent stages of their transmission, to apply correction codes that provide protection against possible errors arising from the action of interference in the communication channel. At the same time, it is important that, with the required correcting ability, these codes have the maximum possible speed. The article presents the results of calculations for linear codes, showing their really achievable limiting capabilities.

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Improved binary codes and sequence families from Z/sub 4/-linear codes

IEEE Transactions on Information Theory ◽

10.1109/18.532904 ◽

1996 ◽

Vol 42 (5) ◽

pp. 1582-1587 ◽

Cited By ~ 30

Author(s):

A.G. Shanbhag ◽

P. Vijay Kumar ◽

T. Hellesath

Keyword(s):

Linear Codes ◽

Binary Codes

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New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830919500575 ◽

2019 ◽

Vol 11 (05) ◽

pp. 1950057

Author(s):

Sara Ban ◽

Dean Crnković ◽

Matteo Mravić ◽

Sanja Rukavina

Keyword(s):

Incidence Matrix ◽

Linear Codes ◽

Minimum Weight ◽

Hadamard Matrices ◽

Binary Codes ◽

Type Ii ◽

Hadamard Design ◽

Binary Linear Codes ◽

Type Formula ◽

Hadamard Designs

For every Hadamard design with parameters [Formula: see text]-[Formula: see text] having a skew-symmetric incidence matrix we give a construction of 54 Hadamard designs with parameters [Formula: see text]-[Formula: see text]. Moreover, for the case [Formula: see text] we construct doubly-even self-orthogonal binary linear codes from the corresponding Hadamard matrices of order 32. From these binary codes we construct five new extremal Type II [Formula: see text]-codes of length 32. The constructed codes are the first examples of extremal Type II [Formula: see text]-codes of length 32 and type [Formula: see text], [Formula: see text], whose residue codes have minimum weight 8. Further, correcting the results from the literature we construct 5147 extremal Type II [Formula: see text]-codes of length 32 and type [Formula: see text].

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The structure of ℤ2ℤ2s-additive cyclic codes

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500489 ◽

2018 ◽

Vol 10 (04) ◽

pp. 1850048 ◽

Cited By ~ 3

Author(s):

Ismail Aydogdu ◽

Taher Abualrub

Keyword(s):

Linear Codes ◽

Cyclic Code ◽

Cyclic Codes ◽

Optimal Parameter ◽

Binary Codes ◽

Binary Linear Codes ◽

Additive Codes

[Formula: see text]-additive codes for any integer [Formula: see text] are considered as codes over mixed alphabets. They are a generalization of binary linear codes and linear codes over [Formula: see text] In this paper, we are interested in studying [Formula: see text]-additive cyclic codes. We will give the generator polynomials of these codes. We will also give the minimal spanning sets for these codes. We will define separable [Formula: see text]-additive codes and provide conditions on the generator polynomials for a [Formula: see text]-additive cyclic code to be separable. Finally, we present some examples of optimal parameter binary codes obtained as images of [Formula: see text]-additive cyclic codes.

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ON THE GENERALISATION OF SIDEL’NIKOV’S THEOREM TO -ARY LINEAR CODES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972719000637 ◽

2019 ◽

Vol 101 (1) ◽

pp. 157-162

Author(s):

YILUN WEI ◽

BO WU ◽

QIJIN WANG

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Linear Codes ◽

Cumulative Distribution ◽

Standard Normal Distribution ◽

Binary Codes ◽

Normal Distribution Function ◽

Code Length ◽

Standard Normal Distribution Function ◽

Standard Normal

We generalise Sidel’nikov’s theorem from binary codes to $q$-ary codes for $q>2$. Denoting by $A(z)$ the cumulative distribution function attached to the weight distribution of the code and by $\unicode[STIX]{x1D6F7}(z)$ the standard normal distribution function, we show that $|A(z)-\unicode[STIX]{x1D6F7}(z)|$ is bounded above by a term which tends to $0$ when the code length tends to infinity.

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Linear, cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2

Filomat ◽

10.2298/fil1405897o ◽

2014 ◽

Vol 28 (5) ◽

pp. 897-906

Author(s):

Ödemiş Özger ◽

Ümmü Kara ◽

Bahattin Yıldız

Keyword(s):

Linear Codes ◽

Gray Map ◽

Binary Codes ◽

Constacyclic Codes ◽

Weight Enumerators ◽

Lee Weight ◽

Macwilliams Identities

In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over S4 are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over S4.

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Ultimate resolution and information in electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100086787 ◽

1991 ◽

Vol 49 ◽

pp. 496-497

Author(s):

D. Van Dyck

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Transfer Function ◽

Information Transfer ◽

Communication Channel ◽

Structural Information ◽

Information Rate ◽

Noise Power ◽

Signal Power ◽

Imaging Device

An (electron) microscope can be considered as a communication channel that transfers structural information between an object and an observer. In electron microscopy this information is carried by electrons. According to the theory of Shannon the maximal information rate (or capacity) of a communication channel is given by C = B log2 (1 + S/N) bits/sec., where B is the band width, and S and N the average signal power, respectively noise power at the output. We will now apply to study the information transfer in an electron microscope. For simplicity we will assume the object and the image to be onedimensional (the results can straightforwardly be generalized). An imaging device can be characterized by its transfer function, which describes the magnitude with which a spatial frequency g is transferred through the device, n is the noise. Usually, the resolution of the instrument ᑭ is defined from the cut-off 1/ᑭ beyond which no spadal information is transferred.

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Method for measuring distortions of a speech signal during its transmission over a communication channel to a biometric identification system

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2020-11-65-72 ◽

2020 ◽

pp. 65-72

Author(s):

V. V. Savchenko ◽

A. V. Savchenko

Keyword(s):

Speech Signal ◽

Communication Channel ◽

Speaker Identification ◽

A Priori ◽

Small Samples ◽

Practical Implementation ◽

Identification System ◽

New Information ◽

Discrimination Criterion ◽

A Priori Uncertainty

This paper is devoted to the presence of distortions in a speech signal transmitted over a communication channel to a biometric system during voice-based remote identification. We propose to preliminary correct the frequency spectrum of the received signal based on the pre-distortion principle. Taking into account a priori uncertainty, a new information indicator of speech signal distortions and a method for measuring it in conditions of small samples of observations are proposed. An example of fast practical implementation of the method based on a parametric spectral analysis algorithm is considered. Experimental results of our approach are provided for three different versions of communication channel. It is shown that the usage of the proposed method makes it possible to transform the initially distorted speech signal into compliance on the registered voice template by using acceptable information discrimination criterion. It is demonstrated that our approach may be used in existing biometric systems and technologies of speaker identification.

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