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Honold T., Kiermaier M., Landjev I. (2020) New upper bounds on the maximal size of an arc in a projective Hjelmslev plane, Proc. 17th International Workshop on Algebraic and Combinatorial Coding Theory, Oct. 11-17, 2020, Bulgaria, IEEE Xplore, 2021, pp. 67-76
Abstract
In this paper we present new upper bounds on the size of an arc in the projective Hjelslev planes PHG(2, R), where R is a chain ring of mutilicity index 2.
Full-text ISBN, DOI
ISBN: 978-1-6654-0287-3 (electronic), DOI: 10.1109/ACCT51235.2020.9383345
Tsvetkov B., Jeliazkov J., Kostadinov H. (2020) Modern Software Lifecycle Management leveraging the power of Blockchain, Proc. 17th International Workshop on Algebraic and Combinatorial Coding Theory, Oct. 11-17, 2020, Bulgaria, IEEE Xplore, 2021, pp. 145-149
Abstract
Many distributed ledger technologies (DLT) offer smart contract platforms, that are already used in various industries such as healthcare, transportation, government, banking, and insurance. Software Lifecycle Management (SLM) is another area where DLT and smart contract platforms could play an important role in the future. SLM processes are covering the initial setup, technical and business configuration and ongoing maintenance of software systems that often consist of many cloud services, on-premise servers, and/or edge devices, spread on many geographical locations. In SLM there are many participants that should communicate each other to achieve common goal, for example the software provisioning. In case something wrong happens in their communication, it is very hard to prove what is the reason and which party failed to deliver, since the environment is complex and the protocols of responsibilities are not bound to the software dependencies. The purpose of this paper is to demonstrate how DLT-based smart contract platforms supports SLM processes for complex business systems where various participants are involved.
Full-text ISBN, DOI
ISBN: 978-1-6654-0287-3 (electronic), DOI: 10.1109/ACCT51235.2020.9383401
Bouyukliev I., Bouyuklieva S. (2022) About Code Equivalence - a Geometric Approach, New Horizons in Differential Geometry and its Related Fields, Edited By: Toshiaki Adachi (Nagoya Institute of Technology, Japan) and Hideya Hashimoto (Meijo University, Japan), World Scientific, 2022, pp. 91-103
Abstract
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for equivalence of linear codes, based on their relation to multisets of points in a projective geometry.
Full-text ISSN, DOI
p-ISSN: 978-981-124-809-2, e-ISSN: 978-981-124-811-5,
DOI: 10.1142/9789811248108_0006
Jeliazkov J., Tsvetkov B., Kostadinov H., Decentralized Research Incentivization System, Studies in Computational Intelligence, Springer, accepted
ISBN, SJR
p-ISSN: 1860-949X, e-ISSN: 1860-9503, SJR: 0.237 (2021)
Borissov L., Borissov Y. (2022) A note on the irrationality of angles of Kloosterman sums over finite field, Comptes rendus de l'Académie bulgare des Sciences, Vol. 75, Issue № 5, pp. 649-654, 2022
Abstract
We prove that the angles of Kloosterman sums over arbitrary finite field are incommensurable with the constant \(\pi\).
Full-text ISSN, SJR, IF, DOI
p-ISSN: 1310–1331, e-ISSN: 2367–5535, SJR: 0.244 (2020), IF: 0.378 (2020),
DOI: 10.7546/CRABS.2022.05.03
Tsvetkov B., Kostadinov H., Software Lifecycle Based on DLT, Communications in Computer and Information Science, Springer, accepted
ISBN, SJR
p-ISSN: 1865-0929, e-ISSN: 1865-0937, SJR: 0.209 (2021)
Alexandrova T., Kostadinov H., Manev N., Watermarking Audio Content: Data Embedding based on Fast Fourier Transform, Studies in Computational Intelligence, Springer, accepted
Abstract
The possibility of embedding watermarks robust against compression in musical audio files is investigated in this paper. The compression itself can be considered as a communication channel whose statistical characteristics are sensitive to the compressed musical genre. We study the compression format Advance Audio Coding (AAC) and collect statistical data for different musical genres. AAC is designed to be the successor of the MP3 format and it generally achieves better sound quality than MP3 format at the same bit rate. AAC is the default audio format for the most modern devices and platforms that dominates in recent years.
    The process of embedding and retrieving a watermark can be regarded as a binary communication channel. In our previous work we investigated an embedding method based on wavelet transformation of the target audio file. In this work we replace the wavelet transformation with Fast Fourier Transform preserving other stages of investigation unaffected.
    We are going to make a comprehensive investigation of an embedding technique applied to musical files which will be subject of subsequent AAC compression. We aim to propose a method of choosing embedding parameters so that to achieve acceptable probability of errors without perceptible loss of quality of the audio file.
ISBN, SJR
p-ISSN: 1860-949X, e-ISSN: 1860-9503, SJR: 0.237 (2021)
Boyvalenkov P., Dragnev P., Hardin D., Saff E., Stoyanova M. (2023) On polarization of spherical codes and designs, Journal of Mathematical Analysis and Applications, Vol. 524, Issue № 1, 2023, 127065
Abstract
In this article we investigate the N-point min-max and max-min polarization problems on the sphere for a large class of potentials in Rn. We derive universal lower and upper bounds on the polarization of spherical designs of fixed dimension, strength, and cardinality. The bounds are universal in the sense that they are a convex combination of potential function evaluations with nodes and weights independent of the class of potentials. As a consequence of our lower bounds, we obtain the Fazekas-Levenshtein bounds on the covering radius of spherical designs. Utilizing the existence of spherical designs, our polarization bounds are extended to general configurations. As examples we completely solve the min-max polarization problem for 120 points on S3 and show that the 600-cell is universally optimal for that problem. We also provide alternative methods for solving the max-min polarization problem when the number of points N does not exceed the dimension n and when N = n + 1. We further show that the cross-polytope has the best max-min polarization constant among all spherical 2-designs of N = 2n points for n = 2, 3, 4; for n ≥ 5, this statement is conditional on a well-known conjecture that the cross-polytope has the best covering radius. This max-min optimality is also established for all so-called centered codes.
Full-text ISSN, SJR, IF, DOI
p-ISSN: 0022-247X, e-ISSN: 1096-0813, SJR: 0.859 (2021), IF: 1.417 (2021),
DOI: 10.1016/j.jmaa.2023.127065
Topalova S., Zhelezova S. (2023) Transitive Deficiency One Parallelisms of PG(3, 7), Mathematics 2023, 11, 2458
Abstract
Consider the n-dimensional projective space PG(𝑛,𝑞) over a finite field with q elements. A spread in PG(𝑛,𝑞) is a set of lines which partition the point set. A parallelism is a partition of the set of lines by spreads. A deficiency one parallelism is a partial parallelism with one spread less than the parallelism. A transitive deficiency one parallelism corresponds to a parallelism possessing an automorphism group which fixes one spread and is transitive on the remaining spreads. Such parallelisms have been considered in many papers. As a result, an infinite family of transitive deficiency one parallelisms of PG(𝑛,𝑞) has been constructed for odd q, and it has been proved that the deficiency spread of a transitive deficiency one parallelism must be regular, and its automorphism group should contain an elation subgroup of order \(𝑞^2\). In the present paper we construct parallelisms of PG(3,7) invariant under an elation group of order 49 with some additional properties, and thus we succeed to obtain all (46) transitive deficiency one parallelisms of PG(3,7). The three parallelisms from the known infinite family are among them. As a by-product, we also construct a much bigger number (55,022) of parallelisms which have the same spread structure, but are not transitive deficiency one.
Full-text ISSN, SJR, IF, DOI
e-ISSN: 2227-7390, SJR: 0.446 (2022), IF: 2.592 (2021) Q1,
DOI: 10.3390/math11112458
Landjev I., Rousseva A., Rogachev E. (2023) Characterization of Some Blocking Sets in PG(4,3), Proceedings of the Int. Conf. on CSECS, Lecture Notes of ICST, 2023, submitted
Landjev I., Rogachev E. (2023) Sperner’s Theorem for Modules over Finite Chain Rings, Designs, Codes and Cryptography, 2023, submitted
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