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Öğe Approaching the Minimum Distance Problem by Algebraic Swarm-Based Optimizations(Dergipark, 2021) Şahinkaya, Serap; Üstün, DenizIn 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]Öğe Mutation-Based Algebraic Artificial Bee Colony Algorithm for Computing the Distance of Linear Codes(Dergipark, 2022) Üstün, Deniz; Şahinkaya, Serap; Korban, AdrianFinding the minimum distance of linear codes is a non-deterministic polynomial-time-hard problem and different approaches are used in the literature to solve this problem. Although, some of the methods focus on finding the true distances by using exact algorithms, some of them focus on optimization algorithms to find the lower or upper bounds of the distance. In this study, we focus on the latter approach. We first give the swarm intelligence background of artificial bee colony algorithm, we explain the algebraic approach of such algorithm and call it the algebraic artificial bee colony algorithm (A-ABC). Moreover, we develop the A-ABC algorithm by integrating it with the algebraic differential mutation operator. We call the developed algorithm the mutation-based algebraic artificial bee colony algorithm (MBA-ABC). We apply both; the A-ABC and MBA-ABC algorithms to the problem of finding the minimum distance of linear codes. The achieved results indicate that the MBA-ABC algorithm has a superior performance when compared with the A-ABC algorithm when finding the minimum distance of Bose, Chaudhuri, and Hocquenghem (BCH) codes (a special type of linear codes).Öğe Priestly-Taylor Coefficient Evaluation for Konya Closed Basin(Bilecik Şeyh Edebali Üniversitesi, 2024) Cicibıyık, Alara; Şarlak, Nermin; Üstün, DenizMeasurement of evaporation in the field is difficult and expensive; thus, the empirical evaporation estimation methods have been developed. However, these estimation methods have both advantages and disadvantages. The main disadvantage is that their coefficients were determined by the climatic conditions of the study areas. One of these methods is Penman. The Penman method, accepted as a reference, has reached the closest estimations to the measurement of evaporation in the field of the different parts of the world. However, it needs lots of measured climatic data. The Priestley-Taylor method was derived to reduce the measured data needs of the Penman method. Priestly and Taylor represented the variables such as saturated and actual vapor pressures and wind speed with coefficient of 1.26. The researchers have continued to study on the calibration of the coefficient for their studies’ area since this method has been known to underestimate evaporation value in areas where advection is effective. The present study consists of two stages. First, evaporation was tried to be estimated with these two methods by using the measured climatic data of five meteorological stations in the Konya Closed Basin. Estimated values were evaluated making comparison with the pan measurements. Although slightly higher values were estimated from the pan measurements with each method, the Penman method was found to be relatively more consistent on the basis of statistical indicators. Second, coefficient was obtained as 1.28 for the study area by using three artificial intelligence-based optimization algorithms. The Penman method was used for comparison in this stage. It was concluded that there was no need for any calibration of the coefficient and the original one was found to be valid for the study area as well.
