Öz
Kaynakça
- [1] Ajitha Shenoy, K.B., Biswas, S., Kurur, P.P., Efficacy of the metropolis algorithm for the minimum-weight codeword problem using codeword and generator search spaces, IEEE Trans Evolut Comput., 24(4)(2020).
- [2] Arora, S., Singh, S., A conceptual comparison of firefly algorithm, bat algorithm and cuckoo search, 2013 International Conference on Control, Computing, Communication and Materials (ICCCCM), Allahabad, (2013), 1–4.
- [3] Augot, D., Charpin, P., Sendrier, N., Studying the locator polynomial of minimum weight codewords of BCH codes, IEEE Trans. Info. Theory, 38(1992), 960–973.
- [4] Bland, J.A., Local search optimisation applied to the minimum distance problem, Adv. Eng. Informat., 21(2007), 391–397.
- [5] Bouzkraoui, H., Azouaoui, A., Hadi, Y., New ant colony optimization for searching the minimum distance for linear codes, International Conference on Advanced Communication Technologies and Networking, (2018). doi: 10.1109/COMMNET.2018.8360246
- [6] Gomez-Torrecillas, J., Lobillo, F.J., Navarro, G., Minimum distance computation of linear codes via genetic algorithms with permutation encoding, ACM Communications in Computer Algebra, 52(3)(2018), 71–74.
- [7] Cuellar, M.P., Gomez-Torrecillas, J., Lobillo, F.J., Navarro, G., Genetic algorithms with permutation-based representation for computing the distance of linear codes, arXiv:2002.12330.
- [8] Hogben, L., Handbook of Linear Algebra. Boca Raton, FL, USA: Champman and Hall, 2007.
- [9] MacWilliams, F.J., Sloane, N.J.A., The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1993.
- [10] Ling, S., Xing, C., Coding Theory: A First Course, Cambridge University Press, 2004.
- [11] Santucci, V., Baioletti, M., Milani, A., Algebraic differential evolution algorithm for the permutation flowshop scheduling problem with total flowtime criterion, in IEEE Transactions on Evolutionary Computation, 20(5)(2016), 682–694.
- [12] Shannon, C.E., A mathematical theory of communication, Bell System Technical Journal, 27(1948), 379–423.
- [13] Wolpert, D.H., Macready, W.G, No free lunch theorems for optimization. IEEE Trans Evolut Comput, 1(1997), 67–82.
- [14] Vardy, A., The intractability of computing the minimum distance of a code, IEEE Transactions on Information Theory, 43(6)(1997), 1757–1766.
- [15] Yang, X.S., A New Metaheuristic Bat-Inspired Algorithm, Nature inspired cooperative strategies for optimization, Studies in Computational Intelligence, 43(284), Springer, Berlin, Heidelberg, 2010.
Öz
Finding the minimum distance of linear codes is one of the main problems in coding theory. The importance of the minimum distance comes from its error-correcting and error-detecting capability of the handled codes.
It was proven that this problem is an NP-hard that is the solution of this problem can be guessed and verified in polynomial time but no particular rule is followed to make the guess and some meta-heuristic approaches in the literature have been used to solve this problem.
In this paper, swarm-based optimization techniques, bat and firefly, are applied to the minimum distance problem by integrating the algebraic operator to the handled algorithms.
Anahtar Kelimeler
Minimum distance minimum-weight codeword BCH codes optimization heuristic bat algorithm firefly algorithm
Kaynakça
- [1] Ajitha Shenoy, K.B., Biswas, S., Kurur, P.P., Efficacy of the metropolis algorithm for the minimum-weight codeword problem using codeword and generator search spaces, IEEE Trans Evolut Comput., 24(4)(2020).
- [2] Arora, S., Singh, S., A conceptual comparison of firefly algorithm, bat algorithm and cuckoo search, 2013 International Conference on Control, Computing, Communication and Materials (ICCCCM), Allahabad, (2013), 1–4.
- [3] Augot, D., Charpin, P., Sendrier, N., Studying the locator polynomial of minimum weight codewords of BCH codes, IEEE Trans. Info. Theory, 38(1992), 960–973.
- [4] Bland, J.A., Local search optimisation applied to the minimum distance problem, Adv. Eng. Informat., 21(2007), 391–397.
- [5] Bouzkraoui, H., Azouaoui, A., Hadi, Y., New ant colony optimization for searching the minimum distance for linear codes, International Conference on Advanced Communication Technologies and Networking, (2018). doi: 10.1109/COMMNET.2018.8360246
- [6] Gomez-Torrecillas, J., Lobillo, F.J., Navarro, G., Minimum distance computation of linear codes via genetic algorithms with permutation encoding, ACM Communications in Computer Algebra, 52(3)(2018), 71–74.
- [7] Cuellar, M.P., Gomez-Torrecillas, J., Lobillo, F.J., Navarro, G., Genetic algorithms with permutation-based representation for computing the distance of linear codes, arXiv:2002.12330.
- [8] Hogben, L., Handbook of Linear Algebra. Boca Raton, FL, USA: Champman and Hall, 2007.
- [9] MacWilliams, F.J., Sloane, N.J.A., The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1993.
- [10] Ling, S., Xing, C., Coding Theory: A First Course, Cambridge University Press, 2004.
- [11] Santucci, V., Baioletti, M., Milani, A., Algebraic differential evolution algorithm for the permutation flowshop scheduling problem with total flowtime criterion, in IEEE Transactions on Evolutionary Computation, 20(5)(2016), 682–694.
- [12] Shannon, C.E., A mathematical theory of communication, Bell System Technical Journal, 27(1948), 379–423.
- [13] Wolpert, D.H., Macready, W.G, No free lunch theorems for optimization. IEEE Trans Evolut Comput, 1(1997), 67–82.
- [14] Vardy, A., The intractability of computing the minimum distance of a code, IEEE Transactions on Information Theory, 43(6)(1997), 1757–1766.
- [15] Yang, X.S., A New Metaheuristic Bat-Inspired Algorithm, Nature inspired cooperative strategies for optimization, Studies in Computational Intelligence, 43(284), Springer, Berlin, Heidelberg, 2010.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik, Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 13 Sayı: 1 |