IAES Inter national J our nal of Articial Intelligence (IJ-AI) V ol. 14, No. 2, April 2025, pp. 1077 ∼ 1086 ISSN: 2252-8938, DOI: 10.11591/ijai.v14.i2.pp1077-1086 ❒ 1077 New family of err or -corr ecting codes based on genetic algorithms El Mehdi Bellfkih 1 , Said Nouh 1 , Imrane Chemseddine Idrissi 1 , Khalid Louartiti 2 , J amal Mouline 1 1 Department of Mathematics and Computer Science, F aculty of Science Ben M’ sick, Uni v ersity Hassan II, Casablanca, Morocco 2 Department of Mathematical Sciences and Decision Support, ENSA, Abdelmalek Essa ˆ adi Uni v ersity , T etouan, Morocco Article Inf o Article history: Recei v ed No v 28, 2023 Re vised No v 17, 2024 Accepted No v 24, 2024 K eyw ords: Decoding Design Error -correcting codes Generator v ector Genetic algorithm Minimum distance ABSTRA CT This paper introduces a no v e l error -correcting code (ECC) construction and decoding approach utilizing genetic algorithms (GAs). Classical ECCs often struggle with ef cienc y in correcting multiple errors due to time-consuming matrix-based encoding and decoding process es. Our GA-based method opti- mizes generator v ect ors to maximize the minimum distance between code w ords, enhancing error correction capabilities. Specically , we construct a ne w f amily of ECCs with code length 31 , dimension 12 , and minimum distance 7 , reducing comple xity from O ( k n ) to O ( k ( n − k )) by encoding message blocks with v ec- tors instead of matrices. In the decoding phase, the GA ef fecti v ely corrects errors in recei v ed code w ords. Experimental results sho w that at a signal-to-noise ratio (SNR) of 7 . 7 dB, our method achie v es a bit error rate ( BER) of 10 − 5 after only 9 generations of the GA. These result s demonstrate impro v ed error correction and decoding performance compared to traditional methods. This study con- trib utes an inno v ati v e approach using GAs for e rror correction, of fering simpler encoding and rob ust performance in coding schemes. This is an open access article under the CC BY -SA license . Corresponding A uthor: El Mehdi Bellfkih Department of Mathematics and Computer Science, F aculty of Science Ben M’ sick, Uni v ersity Hassan II Casablanca, Morocco Email: elmehdi.bellfkih@gmail.com 1. INTR ODUCTION The transmission and storage of information are susceptible to corrupt ion due to v arious ph ysical or logical f aults, which can res u l t in system-wide f ailures. T o mitig ate such risks, rob ust testing and f ault tolerance mechanisms are essential for ensuring secure and stable communication o ws. Error -correcting codes (ECCs) play a pi v otal role in safe guarding data inte grity and reliability by incorporating redundant information into transmitted messages. The ef cac y of ECCs lies in their ability to detect and/or correct errors that may arise during data transmission or storage. This error -correction capability is crucial for maintaining data inte grity under adv erse conditions. While linear block codes, such as Hamming codes, of fer decent error -correction capability , the y are inherently lim ited in their scope. In contrast, nonlinear block codes, e x emplied by turbo codes, e xhibit superior error -correction capabilities b ut are accompanied by higher decoding comple xities [1], [2]. As sho wn in the Figure 1, the minimum distance of a code is directly related to its error detection and correction capability . A code with a lar ger minimum distance can detect and correct more errors compared to a code with a smaller minimum distance. J ournal homepage: http://ijai.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
1078 ❒ ISSN: 2252-8938 Figure 1. Correlating minimum Hamming distance with error detection and correction capabilities In the realm of ECC construction, linear block codes, grounded in linear algebra, are reno wned for their simplicity of implementation, analysis, and comprehension. The y e xcel at detecting and correcting errors within a conned bit range. Examples include Hamming codes, Reed-Solomon codes, and Bose-Chaudhuri- Hocquenghem (BCH) codes. Con v ersely , nonlinear block codes present a more intricate landscape, demanding deeper analytical understanding and implementation ef forts. Y e t, the y boast broader error -correcting capabili- ties, ef fecti v ely managing errors across a lar ger bit spectrum. Notable e xamples encompass Reed-Mulle r codes, Golay codes, and BCH codes. Ho we v er , despite the adv ancements in ECC design, the process of decoding remains a challenging task. T raditional decoding methods often encounter computational bottlenecks, particularly when deal ing with comple x codes. Herein lies the potential for emplo ying metaheuristic approaches to decode ECCs ef ciently . Metaheuristic algorithms, reno wned for their adaptability and problem-solving pro wess, of fer a promising a v enue for tackling the intricacies of ECC decoding. By le v eraging metaheuristic techniques, such as genetic algorithms (GAs), simulated annealing, or particle sw arm optimization, researchers can e xplore no v el decoding strate gies capable of surmounting the comple xities associated with ECCs. There is v arious classes of codes in coding theory , and v arious method to construct them aiming to achie v e the best results e.g., the reliable communication, better comple xity , easy construction of code. Let F 2 be a eld of order 2 and F k 2 be a v ector space of length k . Here we present our ne w k-dimensional binary linear code C o v er F n 2 whose G is its generator matrix, or g ( x ) is its polynomial generator (the ro ws of G for m a basis for C ). [ n, k , d ] 2 denotes a 2-ary linear code with length n , dimenion k and minimum distance d . An element of C is called a code w ord, its weight is the number of nonzero coordinate. The minimum distance of C is the smallest Hamming distance between distinct code w ords (is also the smallest weight in case of binary linear codes) denoted by d( C ). The Singleton bound as in (1) states that a ( n, k , d ) -code or [ n, k , d ] -code satisfy . d ( C ) ≤ n − k + 1 (1) A code with linearity condition and achie v es the equalit y in the Singleton bound is called maximum distance separable (MDS) code. T o achie v e the goal of nding high-performing ECC, our approach tak es adv antage of the optimization nature of the problem. By formulating the problem as an optimization problem, we can le v erage the po wer of optimization algorithms, such as GAs [3], [4], to search for the best possible solutions. The GA frame w ork allo ws us to ef ciently e xplore the v ast solution space and nd good ECC with high minimum distances, making it an ideal approach for this type of problem. GAs are a type of optimization algorithm that is inspired by the process of natural selection and e v olution [5]. GAs are used to solv e comple x problems by simulating the process of e v olution, where a population of potential solutions e v olv es o v er time to w ards an optimal solution [6]–[9]. The y w orks by representing a problem as a set of candidate solutions, also kno wn as a population. Each candidate solution is encoded as a string of parameters, called a chromosome. The chromosomes in the population are then e v aluated using a tness function that assigns a numerical score to each chromosome based on ho w well it solv es the problem. The chromosomes with the highest tness scores are selected as parents and used to produce of fspring, which are ne w candidate solutions, through a process called crosso v er . In this process, the genetic information from the parent chromosomes is combined to produce Int J Artif Intell, V ol. 14, No. 2, April 2025: 1077–1086 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1079 a ne w chromosome (child). This process is repeated o v er se v eral generations, leading to the e v olution of the population to w ards better solutions. GAs also include a mechanism for introducing random v ariations into the population, called mutation. This allo ws the algorithm to e xplore ne w re gions of the solution space and helps to pre v ent getting stuck in local optima. The y are well-suited for problems that ha v e multiple solutions or where the solution space is comple x and dif cult to e xplore using traditional optimization methods. In the ne xt section, we will consider related research ndings to conte xtualize and augment our study’ s conclusions. 2. RELA TED W ORKS The eld of ECCs plays a crucia l role in ensuring data inte grity and reliability in v arious applicati ons. Despite the widespread use of e xisting ECCs, there are challenges that hinder their ef cienc y , partic ularly in terms of the time-consuming encoding and decoding processes. T o address these limitations, researchers ha v e turned to inno v ati v e approaches such as GA for code design and decoding. GA of fer a promising a v enue for generating codes with high minimum distances, thus enhancing error detection and correction capabil ities. A range of studies ha v e e xplored the design and decoding of ECC [10]–[12]. Natarajan et al. [13] de v eloped algebraic ECC for informed recei v ers, while Elk elesh et al. [11] proposed a GA-based lo w density parity check (LDPC) code design scheme. Das and T ouba [14] introduced a ne w class of single b urst ECC with parallel decoding, and Zhang et al. [15] presented a decoding algorithm for v e-error -correcting binary quadratic residue codes. These studies collecti v ely contrib ute to the adv ancement of ECC, with a focus on informed recei v ers, LDPC codes, b urst error correction, and decoding algorithms. McGuire and Sabin [16] ha v e emplo yed GA to search for linear binary codes with optimal minim um distance. In another paper , Maini et al. [17] de v eloped suboptimal soft decision decoders for linear block codes. GA ha v e also been utilized to tackle the problem of nding ECCs that correct a maximum number of errors [18]. These studies highlight the ef fecti v eness of GA in addressing v arious aspects of error correction code design and decoding, and recognized as one of the most po werful optimization methods due to its v er - satility and ease of implementation across v arious problem domains. One of the k e y strengths of GA lies in their di v erse set of operators and options, which allo w for e xible e xploration and e xploitation of the search space [19]–[21]. These operators, including selection, crosso v er , and mutation, pro v i de a rich toolbox that can be tailored to specic optimization problems. Moreo v er , the GA ’ s inherent parallelism and population- based nature enable it to ef fecti v ely handle comple x and multimodal optimization landscapes. In f act, it can be vie wed as a v ariant of the minimum distance problem, which is kno wn to be NP-hard. The minimum distance of a code plays a crucial role in its error detection and correction capabilities. Ho we v er , determin- ing the e xact minimum distance of a code is computationally comple x and requires e xhausti v e search o v er all code w ords. This computational hardness moti v ates the e xploration of heuristic approaches, such as GA, to ef ciently search for codes with lar ge minimum distances. The design of ECCs has traditionally relied on coding-theoretic principles, aiming to optimize code properties such as minimum Hamming distance and de- coding threshold. Ho we v er , recent adv ancements ha v e e xplored the application of articial intelligence (AI) techniques, particularly GA, for ECC design. Huang et al. [10] in v estig ate an AI-dri v en approach using GA to design optimal codes within specic f amilies, sho wcasing comparable performance to e xisting codes and e v en superior performance in certain cases. Amirzadeh et al. [22] focus on joint GA and linear program- ming optimization for LDPC codes, stri ving for lo w comple xity , high coding threshold, and decoding stability . Mahran [23] e xplores the optimization of turbo product c o de s (TPC) parameters using GA, nding a balance between error performance and code comple xity . Joundan et al. [24] present a GA approach for designing linear codes with lar ge minimum weight and small dual minimum distance, demonstrating ef fecti v e error correction performance. These studies collecti v ely highl ight the potential of GA in ECC design, of fering opportunities for impro ving code performance, comple xity , and error correction capabilities in v arious communication systems. GAs ha v e em er ged as a po werful tool for ECCs decoding. Chaibi et al. [25] present a GA-based decoder for LDPC codes, demonstrating its superior performance compared to the sum-product decoder . Azouaoui et al. [26] propose hard-decision and soft-decision decoding techniques based on GAs for general ECC, sho wcasing their ef fecti v eness o v er v arious transmission channels. Broul ´ ım et al. [27] e xplore the appli- cation of GA optimization algorithms to design parity-check matrices for LDPC codes, enabling the correction of b urst errors. Nouh et al. [28] focus on decoding block codes using GAs and permutations set, sho wing comparable error correcting performances to e xisting met hod s . Elk elesh et al. [11] present a decoder -tailored polar code design using GAs, achie ving the same error -rate performance as e xisting decoding algorithms while Ne w family of err or -corr ecting codes based on g enetic algorithms (El Mehdi Bellfkih) Evaluation Warning : The document was created with Spire.PDF for Python.
1080 ❒ ISSN: 2252-8938 reducing the decoding comple xity . Berkani et al. [29] propose compact GAs with lar ger tournament size for impro v ed decoding of linear block codes, demonstrating the ef fecti v eness of lar ger tournament sizes in soft decision decoding. These studies collecti v ely highlight the potential of GAs in ECC decoding and code design, of fering enhanced error correction performance, reduced comple xity , and impro v ed decoding capabilities in v arious communication. 3. PR OPOSED METHODS In this section, our GA-based methods are proposed using the principal f actors (tness function, crosso v er , and mutation f actors). we will delv e into the application of GAs based methods in the encoding and decoding phases of ECCs. Specically , we wil l e xplore ho w GAs can be utilized to optimize these cru- cial stages of the coding process. F or the encoding phase, we will discuss the use of GAs based methods to determine optimal generator v ectors, considering f actors such as code properties and encoding comple xity . In the decoding phase, we will e xamine ho w GA based method can aid in nding the corrected corrupted recei v ed w ords, focusing on f actors such as decoding performance, and error correction capability . Through a detailed analysis, we aim to shed light on the main f actors and considerations when emplo ying GA for ef cient encoding and decoding of ECCs. 3.1. Construction phase Our primary objecti v e is to identify a generator v ector that maximizes the distance between encoded messages. By emplo ying GA in the encoding phase, we aim to nd the most suitable generator v ector that enhances error correction capabilities. Ho we v er , we will rely on encoding through multiplying by generator v ector and con v ersion based on binary and decimal. The Figure 2 sho wcases the sequential steps in v olv ed in encoding a message using a generator v ector . The process be gins with the di vision of the message into blocks, represented in decimal form. These blocks are then con v erted into their corresponding binary forms, ensuring that the message is represented using binary digits. The ne xt stage focuses on the encoding process itself. The binary message, consisting of k bits, under - goes multiplication with a generator v ector of n-k bits. This multiplication results in a binary message of length n bits, which represents the encoded message with added redundanc y for error correction or detection. Finally , the encoded message is con v erted back to its original deci mal form. This gure pro vides a clear visualization of the encoding process, emphasizing the transformation from decimal to binary representation, the application of the generator v ector for encoding, and the subsequent con v ersion back to decimal form. Figure 2. Encoding process using generator v ector The diagram in Figure 3 illustrates a GA-based method for nding an optimal generator v ector . The GA operates on a population of candidate generator v ectors, with the number of generations and initial population size specied as input parameters. Elitism is emplo yed as the selection strate gy , ensuring that the ttest indi viduals are preserv ed in each generation. The tness function, dened as the minimum distance achie v ed by a generator v ector , guides the e v aluation and selection process. Crosso v er and mutation operators are applied to introduce di v ersity and e xplore ne w solutions within the population. The initial population con- sists of generator v ectors with n − k bits, where n is the total number of code-w ord bits and k is the number of message bits. The GA iterati v ely e v olv es the population to con v er ge to w ards an optimal generator v ector that maximizes the minimum distance. f g en = min { d ( C ) : C = { bw i × g en, ∀ i < 2 k }} (2) Where bw i are messages of k bits and gen is a generator v ector of n-k bits. Int J Artif Intell, V ol. 14, No. 2, April 2025: 1077–1086 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1081 Figure 3. Diagram of the method based on the GA to nd the generator v ector for an ECC The pro vided Figure 4 demonstrates the crosso v er operation in our GA-based method. If a randomly generated probability is less than or equal to a predened v alue ( p m = 0 . 97 ), the crosso v er is applied. T w o parent indi viduals, each represented by a binary sequence of n bits, are selected based on tness function v alue as mentioned in (2). A random position, denoted as p, is chosen within the length of the sequence. The rst child is created by combining the section from the rst parent starting from position 0 up to position p, with the section from the second parent starting from position p up to position n. Similarly , the second child is formed by combining the section from the second parent from position 0 to p, and from the rst parent from position p to n. Additionally , the gure indicates that the mutation operation follo ws a similar principle. If a randomly generated number between 0 and 1 is less than or equal to a predened v alue ( p c = 0 . 02 ), the mutation occurs. It in v olv es ipping the v alue at a specic position in the child’ s binary sequence. Figure 4. Crosso v er and mutation f actors 3.2. Decoding phase W e present a GA-based method for correcting corrupted recei v ed code-w ords in ECCs. Our ob j ec- ti v e is to accurately reco v er the original information from the recei v ed w ord, e v en in the presence of errors. The proposed method utilizes GA to iterati v ely search for the optimal solution that con v er ge to the correct code-w ord. f codew or d = d ( r eceiv edw or d, codew or d ) (3) Ne w family of err or -corr ecting codes based on g enetic algorithms (El Mehdi Bellfkih) Evaluation Warning : The document was created with Spire.PDF for Python.
1082 ❒ ISSN: 2252-8938 The diagram in Figure 5 illustrates a GA-based method for decoding recei v ed w ords in ECCs. The algorithm tak es se v eral inputs, including the length n and dimension k of the ECC, the number of corrections allo wed t, the number of generations for the algorithm to iterate, and the initial population consisting of code- w ords generated using the a v ailable generator v ectors. Elitism is emplo yed as the selection strate gy , and the tness function is dened as the minimum distance between the recei v ed w ord and the code-w ords as in (3) in the population. The crosso v er and mutation operations are applied with specic rates and with the same strate gy as sho wn in the Figure 4, aiming to e xplore and e xploit the solution space. The initial population is initialized with generator v ectors of size n-k bits. Through the iterations of the GA, the m ethod aims to decode the recei v ed w ord and reco v er the original information accurately . Figure 5. Diagram of the method based on the GA for decoding ne w ECCs 4. RESUL TS AND DISCUSSION In this section, we present the results obtained from our study on the construction and decoding of ECCs. The subsections belo w detail the outcomes of our in v estig ations into both the construction and decoding phases, highlighting the performance and ef c ac y of our proposed methodologies. Through rigorous e xperimentation and analysis, we assess the ef fecti v eness of our approach in achie ving rob ust error correction capabilities and ef cient decoding processes. 4.1. Construction of err or -corr ecting codes The pro vided T able 1 outl ines the def ault parameters used in running the GA-based method for nding the generator v ector of the ECC with a length of 31 and a dimension of 12. These parameters, which include settings such as populati on size, crosso v er rate, and mutation probability , serv e as the initial congurations for the GA, pro viding a starting point for the optimization process. By carefully selecting these def ault parameters, the algorithm ef ciently na vig ates the search space to identify generator v ectors that maximize the minimum distance between code w ords, thereby enhancing the ECC’ s error -correcting capabilities. After running the GA-based method with the def ault parameters mentioned in T able 1, we obtained a set of generator v ectors for an ECC of length 31 and dimension 26. The T able 2 results include the minimum distance achie v ed by these generator v ectors, which is equal to the kno wn lo wer bound. This suggests that the GA ef fecti v ely identied generator v ectors that of fer optimal error correction capabilities for the gi v en ECC dimensions. Int J Artif Intell, V ol. 14, No. 2, April 2025: 1077–1086 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1083 T able 1. The def ault parameters for GA based method for codes of moderate lengths P arameter v alue Initial population size 20000 Selection elitism Crosso v er rate 0.93 Mutation rate 0.02 Number of generations 50 T able 2. Set of ECCs of parameters (31,12) n k d Generator 31 12 7 1110001001011000001 31 12 7 1110000111101100101 31 12 7 1101001101011000101 31 12 7 1010000110111010111 31 12 7 1110010110100100101 31 12 7 1011100111111000111 31 12 7 1111011100111010011 31 12 7 1111010010101000111 31 12 7 1111100110001111011 31 12 7 1111111010010011001 31 12 7 1111001011000011001 31 12 7 1110101001111100111 31 12 7 1111110111011010011 31 12 7 1110100010101001111 The application of the GA-based approach resulted in the disco v ery of ECCs with dimension 12 and length 31, sho wcasing minimum distances that equal to the kno wn lo wer bound. This signicant achie v ement holds promising implications for error detection and correction in practical scenarios. These codes e xhibit an e xceptional capability to detect and correct errors, surpassing the performance of pre viously kn o wn codes. The listed codes in T able 2 e x emplify superior error -correcting properties, indicating their potential for enhancing data inte grity and ensuring reliable information transmission and storage. Also, Our GA based method has successfully identied optimal generator v ectors, enabling a more ef cie n t encoding process. Instead of multi- plying message blocks of length k by a matrix of dimension (k,n), we no w multiply them by a v ector of length n-k. This reduction in dimensionality results in signicant comple xity g ains, leading to impro v ed ef cienc y in the encoding process. The results are summarized in the T able 3. T able 3. Encoding comple xity Encoding process Comple xity Encoding via generator matrix O ( k n ) Encoding via generator v ector O ( k ( n − k )) 4.2. Decoding After successfully nding a set of generator v ectors that maximize the error -correcting capabiliti es of our ECCs, we proceed to the decoding phase, where we introduce a GA-based method for decoding these ne w codes. This method le v erages GA to ef ciently correct errors in the recei v ed code w ords by e xploring possible solutions and selecting the most optimal one based on a tness function. The focus of this section is on e v aluating the bit error rate (BER) performance of the decoding process, demonstrating ho w ef fecti v ely our GA-based decoder restores the original messages under v arious le v els of noise. The T able 4, presents the chosen def ault parameters for the GA-based decoding method include a relati v ely small population size and a limited number of generations. This decision w as made to ensure a manageable computational comple xity during the decoding process. Our algorithm is designed to create a population of candidate w ords deri v ed from a recei v ed w ord. Specically , the algorithm generates a set of I n itP op w ords closely related to the input recei v ed w ord. Additionally , we implement an adjustment by increasing the minimum allo w able distance between generated w ords. These tw o strate gic steps collecti v ely serv e to reduce algorithmic comple xity and enhance computational ef cienc y in terms of speed. Furthermore, in instances where corre ction of t he recei v ed w ord is not feasible due to an error count surpassing the predened Ne w family of err or -corr ecting codes based on g enetic algorithms (El Mehdi Bellfkih) Evaluation Warning : The document was created with Spire.PDF for Python.
1084 ❒ ISSN: 2252-8938 threshold v alue (t), the algorithm pro vides a set of proximate w ords. This information pro v es v aluable in scenarios where understanding the proximity of the recei v ed data is of signicance. T able 4. The def ault parameters for GA based method for decoding ECCs P arameter V alue Initial population size 500 Selection elitism Crosso v er rate 0.93 Mutation rate 0.07 Number of generations 1000 The Figure 6 illustrates the e xceptional decoding performances of our method for our found code with a length of 31, dimension 12, and a minimum distance of 7. Notably , at an signal-to-noise ratio (SNR) of 7.7 dB, the BER stands at 10 − 5 , highlighting the decoder’ s initial performance. As the SNR increases to 8.5 dB, the BER de creases to 10 − 6 , underscoring the decoder’ s enhanced error -correcting capabilities with impro v ed SNR. This progression signies the decoder’ s ef fecti v eness in achie vi ng higher le v els of data accurac y under v arying signal conditions. Figure 6. BER performance of GA-based decoder In spite of the substantial increase in the number of generations as indicated in T able 4, intended to ensure the successful decoding of recei v ed w ords irrespecti v e of the nu m ber of errors, the achie v ed outcomes remain belo w the v alues specied in T able 4. This observ ation is substantiated by the statistical summary presented in T able 5, which pro vides insights into the a v erage and standard de viation. Notably , the lo w v alues of both parameters in T able 5 signify the commendable ef cienc y and ef fecti v eness of our algorithm in the decoding process across v arying SNRs. T able 5. Statistical summary of algorithm performance Number of w ords Max number of generations A vg number of generations Std number of generations 100000 1000 ≈ 8.7 ≈ 8.2 5. CONCLUSION This research article has demonstrated the ef fecti v eness of uti lizing GA-based methods for both the construction and decoding of ECCs. By emplo yi n g these methods, we ha v e successfully identied generator v ectors with high minimum Hamming distances, thereby streamlining the encoding proce ss and enhancing the BER performance of the codes. Ho we v er , we ackno wledge the limitation of achie ving relati v ely lo w rates. Mo ving forw ard, our future objecti v es entail addressing this limitation by optimizing the generat ion of gener - ator v ectors for specied parameters of length n and dimension k, as well as rening our decoder to further Int J Artif Intell, V ol. 14, No. 2, April 2025: 1077–1086 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1085 impro v e the BER performances of the ECCs. Through these endea v ors, we aim to bolster the ef cienc y and ef cac y of ECCs in real-w orld communication and storage systems. REFERENCES [1] A. Said, “Intr oduction to arithmetic coding – theory and practice, ” arXiv-Computer Science , 2023. [2] J. H. V . Lint, “Introduction to coding theory , ” Discr ete Applied Mathematics , Berlin, Ne w Y ork: Springer , v ol. 6, no. 1, 1983, doi: 10.1016/0166-218X(83)90114-2. [3] S. Benghazouani, S. Nouh, and A. Zakrani, “Enhancing breast cancer diagnosis: a comparati v e analysis of feature selec- tion techniques, ” IAES International J ournal of Articial Intellig ence (IJ-AI) , v ol. 13, no. 4, pp. 4312–4322, 2024, doi: 10.11591/ijai.v13.i4.pp4312-4322. [4] K. Kangra and J. 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Ne w family of err or -corr ecting codes based on g enetic algorithms (El Mehdi Bellfkih) Evaluation Warning : The document was created with Spire.PDF for Python.
1086 ❒ ISSN: 2252-8938 BIOGRAPHIES OF A UTHORS El Mehdi Bellfkih holds a Ph.D. in applied mathematics from Hassan II Uni v ersity , specializing in coding theory , error -correcting codes, articial intelligence, and machine learning. His research e xplores inno v ati v e solutions in t hese elds to address comple x computational problems. He can be contacted at email: elmehdi.bellfkih@gmail.com. Said Nouh holds a Ph.D. in computer sciences at National School of Computer Science and Systems Analysis (ENSIAS), Rabat, Morocco in 2014. He is currently professor (higher de gree research (HDR)) at F aculty of sciences Ben M’Sick, Hassan II Uni v ersity , Casablanca, Morocco. His current research interests articial intelligence, machine learning, deep learning, telecommunications, information, and coding theory . He can be contacted at email: said.nouh@uni vh2m.ma. Imrane Chemseddine Idrissi is a Ph.D. in computer science at F aculty of Sciences Ben M’Sik (FSBM), Hassan II Uni v ersity , Cas ablanca, Morocco. He recei v ed a mas ter’ s thesis in data science and big data at ENSIAS Mohammed V uni v ersity in 2019. His current research interests include netw orks and sys tems, telecommunications, information, coding theory , m achine learning, and deep learning. He can be contacted at email: imrane.chemseddine-etu@etu.uni vh2c.ma or im- ran.chems@gmail.com. Khalid Louartiti originally hailing from T aounate, Morocco, he earned his Ph.D. from Sidi Mohamed Ben Abdellah Uni v ersity in Fes, Morocco. Presently serving as a Professor at the National School of Applied Scie nces (ENSA) in T etouan, Morocco. His research focuses on graph theory , modules, ideals, commutati v e algebra, and amalg amat ed algebra. He can be contacted at email: lokha2000@hotmail.com. J amal Mouline originally from Ouaz zane, Morocco, he earned his Ph.D. from Pro v ence Uni v ersity in France. Presently , he holds the position of a Professor in the Department of Mathematics and Informatics at Hassan II Uni v ersity in Morocco. His research focuses on x ed point theory and combinatorial theory . He can be contacted at email: mouline61@gmail.com. Int J Artif Intell, V ol. 14, No. 2, April 2025: 1077–1086 Evaluation Warning : The document was created with Spire.PDF for Python.