A novel genetic search scheme based on nature-inspired evolutionary algorithms for binary self-dual codes-Reference-Cited by-同舟云学术

A novel genetic search scheme based on nature-inspired evolutionary algorithms for binary self-dual codes

Published:2022 Issue:0 Volume:0 Page:0
ISSN:1930-5346
Container-title:Advances in Mathematics of Communications
language:
Short-container-title:AMC

Author:

Korban Adrian¹,Şahinkaya Serap²,Ustun Deniz³

Affiliation:

1. University of Chester, Department of Physical, Mathematical and Engineering Sciences University of Chester, England

2. Tarsus University, Faculty of Engineering, Department of Natural and Mathematical Sciences, Turkey

3. Tarsus University, Faculty of Engineering, Department of Computer Engineering, Turkey

Abstract

<p style='text-indent:20px;'>In this paper, a genetic algorithm, one of the evolutionary algorithm optimization methods, is used for the first time for the problem of computing extremal binary self-dual codes. We present a comparison of the computational times between the genetic algorithm and a linear search for different size search spaces and show that the genetic algorithm is capable of computing binary self-dual codes significantly faster than the linear search. Moreover, by employing a known matrix construction together with the genetic algorithm, we are able to obtain new binary self-dual codes of lengths 68 and 72 in a significantly short time. In particular, we obtain 11 new binary self-dual codes of length 68 and 17 new binary self-dual codes of length 72.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory,Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory

Reference42 articles.

1. K. B. Ajitha Shenoy, S. Biswas and P. P. Kurur, Efficacy of the metropolis algorithm for the minimum-weight codeword problem using codeword and generator search spaces, IEEE Transactions on Evolutionary Computation, 24, (2020), 664–678

2. P. E. Black, Big-O notation, dictionary of algorithms and data structures [online], U.S. National Institute of Standards and Technology, 2008 (accessed 26 November 2009). Available from: http://www.itl.nist.gov/div897/sqg/dads/HTML/bigOnotation.html

3. J. A. Bland.Local search optimisation applied to the minimum distance problem, Adv. Eng. Informat., 21 (2007), 391-397.

4. J. A. Bland, A. T. Baylis.A tabu search approach to the minimum distance of error-correcting codes, Int. J. Electron., 79 (1995), 829-837.

5. M. Bortos, J. Gildea, A. Kaya, A. Korban, A. Tylyshchak.New self-dual codes of length 68 from a $2 \times 2$ block matrix construction and group rings, Adv. Math. Commun., 16 (2022), 269-284.