Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Coding and Combinatorics
share announcement

Coding and Combinatorics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 15409

Special Issue Editor

Prof. Dr. Galina Bogdanova

E-Mail Website
Guest Editor
Department of Mathematical Foundations of Informatics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1040 Sofia, Bulgaria
Interests: codes theory; data bases; data protection; watermarking
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

There are many current scientific challenges in the field of coding theory (sometimes called algebraic coding theory) and the study of the properties of codes and their specific applications.

This Special Issue will gather the latest contributions concerning recent achievements in coding theory and present the latest investigations of error correcting codes, data compression (or source coding), error control (or channel coding), cryptographic coding, line coding, nonlinear codes, watermarking, neural coding, etc.

We invite authors to submit original research papers and high-quality review articles on coding theory and the mathematical methods used, the classical and modern algebraic techniques involving finite fields, group theory and polynomial algebra, the relationships with other areas of discrete mathematics, and others.

Prof. Dr. Galina Bogdanova
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Coding theory
  • Finite fields
  • Optimal codes
  • Error-correcting codes
  • Linear codes
  • Nonlinear codes
  • Equidistant codes
  • Lexicographic codes
  • Neural coding
  • Data protection
  • Data compression
  • Cryptography
  • Watermarking

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

8 pages, 240 KiB  
Article
Enumeration of Optimal Equidistant Codes
by Galina Bogdanova and Todor Todorov
Mathematics 2022, 10(5), 740; https://doi.org/10.3390/math10050740 - 26 Feb 2022
Viewed by 1527
Abstract
Problems of search and enumeration of binary and ternary equidistant codes are considered in the paper. We investigate some combinatorial algorithms and develop specialized computer packages to find non-equivalent optimal binary and ternary equidistant codes for 3 ≤ d ≤ n ≤ 9. [...] Read more.
Problems of search and enumeration of binary and ternary equidistant codes are considered in the paper. We investigate some combinatorial algorithms and develop specialized computer packages to find non-equivalent optimal binary and ternary equidistant codes for 3 ≤ d ≤ n ≤ 9. Full article
(This article belongs to the Special Issue Coding and Combinatorics)
18 pages, 4905 KiB  
Article
Mathematically Based Assessment of the Accuracy of Protection of Cardiac Data Realized with the Help of Cryptography and Steganography
by Galya Georgieva-Tsaneva, Galina Bogdanova and Evgeniya Gospodinova
Mathematics 2022, 10(3), 390; https://doi.org/10.3390/math10030390 - 27 Jan 2022
Cited by 8 | Viewed by 2434
Abstract
This paper describes the application of cryptography and steganography in the protection of cardiac databases. The original cardiac data studied were transformed using a Daubechies wavelet transform. The next step is to conduct Energy Packing Efficiency-based compression. A watermark is added to the [...] Read more.
This paper describes the application of cryptography and steganography in the protection of cardiac databases. The original cardiac data studied were transformed using a Daubechies wavelet transform. The next step is to conduct Energy Packing Efficiency-based compression. A watermark is added to the received data to protect against unauthorized access, before hybrid cryptography is performed using a suitably selected encryption algorithm. The presented and analyzed algorithm includes protection using public and symmetric key cryptography. The proposed software algorithm is performed on real electrocardiographic, photoplethysmographic, and Holter cardio data. We have evaluated the effectiveness of the applied approach and concluded that a sufficient level of protection of the studied data has been achieved, with methods of authentication and accuracy applied to the users. Full article
(This article belongs to the Special Issue Coding and Combinatorics)
►▼ Show Figures

Figure 1

14 pages, 1503 KiB  
Article
Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source
by Jelena Nikolić, Danijela Aleksić, Zoran Perić and Milan Dinčić
Mathematics 2021, 9(23), 3091; https://doi.org/10.3390/math9233091 - 30 Nov 2021
Cited by 3 | Viewed by 1695
Abstract
Motivated by the fact that uniform quantization is not suitable for signals having non-uniform probability density functions (pdfs), as the Laplacian pdf is, in this paper we have divided the support region of the quantizer into two disjunctive regions and utilized the simplest [...] Read more.
Motivated by the fact that uniform quantization is not suitable for signals having non-uniform probability density functions (pdfs), as the Laplacian pdf is, in this paper we have divided the support region of the quantizer into two disjunctive regions and utilized the simplest uniform quantization with equal bit-rates within both regions. In particular, we assumed a narrow central granular region (CGR) covering the peak of the Laplacian pdf and a wider peripheral granular region (PGR) where the pdf is predominantly tailed. We performed optimization of the widths of CGR and PGR via distortion optimization per border–clipping threshold scaling ratio which resulted in an iterative formula enabling the parametrization of our piecewise uniform quantizer (PWUQ). For medium and high bit-rates, we demonstrated the convenience of our PWUQ over the uniform quantizer, paying special attention to the case where 99.99% of the signal amplitudes belong to the support region or clipping region. We believe that the resulting formulas for PWUQ design and performance assessment are greatly beneficial in neural networks where weights and activations are typically modelled by the Laplacian distribution, and where uniform quantization is commonly used to decrease memory footprint. Full article
(This article belongs to the Special Issue Coding and Combinatorics)
►▼ Show Figures

Figure 1

20 pages, 22337 KiB  
Article
Improving DFT-Based Image Watermarking Using Particle Swarm Optimization Algorithm
by Manuel Cedillo-Hernandez, Antonio Cedillo-Hernandez and Francisco J. Garcia-Ugalde
Mathematics 2021, 9(15), 1795; https://doi.org/10.3390/math9151795 - 29 Jul 2021
Cited by 35 | Viewed by 3179
Abstract
Robust digital image watermarking is an information security technique that has been widely used to solve several issues related mainly with copyright protection as well as ownership authentication. In general terms, robust watermarking conceals a small signal called a “watermark” in a host [...] Read more.
Robust digital image watermarking is an information security technique that has been widely used to solve several issues related mainly with copyright protection as well as ownership authentication. In general terms, robust watermarking conceals a small signal called a “watermark” in a host image in a form imperceptible to human vision. The efficiency of conventional robust watermarking based on frequency domain depend directly on the results of performance in terms of robustness and imperceptibility. According to the application scenario and the image dataset, it is common practice to adjust the key parameters used by robust watermarking methods in an experimental form; however, this manual adjustment may involve exhaustive tasks and at the same time be a drawback in practical scenarios. In recent years, several optimization techniques have been adopted by robust watermarking to allowing adjusting in an automatic form its key operation parameters, improving thus its performance. In this context, this paper proposes an improved robust watermarking algorithm in discrete Fourier transform via spread spectrum, optimizing the key operation parameters, particularly the amounts of bands and coefficients of frequency as well as the watermark strength factor using particle swarm optimization in conjunction with visual information fidelity and bit correct rate criteria. Experimental results obtained in this research show improved robustness against common signal processing and geometric distortions, preserving a high visual quality in color images. Performance comparison with conventional discrete Fourier transform proposal is provided, as well as with the current state-of-the-art of particle swarm optimization applied to image watermarking. Full article
(This article belongs to the Special Issue Coding and Combinatorics)
►▼ Show Figures

Figure 1

9 pages, 236 KiB  
Article
Integer Codes Correcting Asymmetric Errors in Nand Flash Memory
by Hristo Kostadinov and Nikolai Manev
Mathematics 2021, 9(11), 1269; https://doi.org/10.3390/math9111269 - 1 Jun 2021
Cited by 2 | Viewed by 2164
Abstract
Memory devices based on floating-gate transistor have recently become dominant technology for non-volatile storage devices like USB flash drives, memory cards, solid-state disks, etc. In contrast to many communication channels, the errors observed in flash memory device use are not random but of [...] Read more.
Memory devices based on floating-gate transistor have recently become dominant technology for non-volatile storage devices like USB flash drives, memory cards, solid-state disks, etc. In contrast to many communication channels, the errors observed in flash memory device use are not random but of special, mainly asymmetric, type. Integer codes which have proved their efficiency in many cases with asymmetric errors can be applied successfully to flash memory devices, too. This paper presents a new construction and integer codes over a ring of integers modulo A=2n+1 capable of correcting single errors of type (1,2),(±1,±2), or (1,2,3) that are typical for flash memory devices. The construction is based on the use of cyclotomic cosets of 2 modulo A. The parity-check matrices of the codes are listed for n≤10. Full article
(This article belongs to the Special Issue Coding and Combinatorics)
15 pages, 2905 KiB  
Article
Application of Delaunay Triangulation and Catalan Objects in Steganography
by Faruk Selimović, Predrag Stanimirović, Muzafer Saračević and Predrag Krtolica
Mathematics 2021, 9(11), 1172; https://doi.org/10.3390/math9111172 - 22 May 2021
Cited by 9 | Viewed by 2737
Abstract
This paper presents a new method of steganography based on a combination of Catalan objects and Voronoi–Delaunay triangulation. Two segments are described within the proposed method. The first segment describes the process of embedding data and generating a complex stego key. The second [...] Read more.
This paper presents a new method of steganography based on a combination of Catalan objects and Voronoi–Delaunay triangulation. Two segments are described within the proposed method. The first segment describes the process of embedding data and generating a complex stego key. The second segment explains the extraction of a hidden message. The main goal of this paper is to transfer a message via the Internet (or some other medium) using an image so that the image remains absolutely unchanged. In this way, we prevented the potential attacker from noticing some secret message hidden in that picture. Additionally, the complex stego key consists of three completely different parts (the image, the encrypted Delaunay triangulation, and the array Rk in Base64 code), which are very difficult to relate with each other. Finally, a few security analyses of the proposed method are conducted, as well as the corresponding steganalysis. Full article
(This article belongs to the Special Issue Coding and Combinatorics)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop