Approaching the Minimum Distance Problem by Algebraic Swarm-Based Optimizations
Yükleniyor...
Tarih
2021
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info:eu-repo/semantics/openAccess
Özet
In 1948, Claude Shannon, published ”A Mathematical Theory of Communication,” a seminal paper, which was about reliable data transmission over noisy channels [12]. Efficient and reliable data transmission, which can be done by some error-control techniques, are one of the main interests of coding theory. Error detecting and correcting capability are very important feature of a code and it is determined by the minimum distance of the code. Computing the minimum distance of a linear code C of large length is a difficult problem in coding theory. In [14], Vardy showed that this computation is an NP-hard type. The problem of finding minimum distance is getting harder when the size of the code grows. Therefore, some meta-heuristic algorithms have been used to approach the problem. In most of the existing literature, genetic algorithms are used for the considered problem. As far as our knowledge, among the
algorithms in the literature that are based on swarm intelligence, only the ant colony algorithm (ACO) was used for the minimum-weight codeword problem [4,5]. It is well known that there is no heuristic algorithm which can perform good enough to solve optimization problems, please see [13] for details. . Therefore, it is natural to try the other swarm-based optimization techniques for the considered problem.
In this paper, bat algorithm (BA) and firefly algorithm (FA) are applied to the minimum distance problem by
integrating the algebraic operator to the handled algorithms. Most of the papers in the literature uses codewords as a search space for the minimum distance problem. Recently, generator matrices were considered as a search space, which turned out to be a better approach than using the codewords as a search space, please see [1] for details. In this work, we also consider generator matrices as a search space. In coding theory, the BCH codes or BoseOCoChaudhuriOCoHocquenghemcodes form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field. Effectiveness of the presented algorithm is controlled by running the algorithm on BCH codes since they are the standard codes with known minimum distance values [3, 9]
Açıklama
Anahtar Kelimeler
Minimum distance, minimum-weight codeword, BCH codes, optimization, heuristic, bat algorithm, firefly algorithm
Kaynak
Turkish Journal of Mathematics and Computer Science
WoS Q Değeri
Scopus Q Değeri
Cilt
13
Sayı
1
Künye
Şahinkaya, S., ve Üstün, D. (2021). Approaching the Minimum Distance Problem by Algebraic Swarm-Based Optimizations. Turkish Journal of Mathematics and Computer Science, 13(1), 129-134. https://doi.org/10.47000/tjmcs.825565
