Abstract
The maximum possible cardinality of a binary code of length n and Hamming distance d is denoted by A(n,d). The current lower bound for A(16,5) is 256, as implied by the Nordstrom–Robinson code. We improve this bound to 258 by presenting a binary code of length 16, minimum distance 5 and cardinality 258. The code is found using a known construction and Tabu Search.
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Brouwer, A.E.: Small binary codes. website at https://www.win.tue.nl/~aeb/codes/binary.html (2018). Accessed 26 November 2018
Dueck, G., Scheuer, T.: Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing. J. Comput. Phys. 90(1), 161–175 (1990)
Fiduccia, C.M., Mattheyses, R.M.: A linear-time heuristic for improving network partitions. In: Proceedings of the 19th Design Automation Conference, pp. 175–181. IEEE Press (1982)
Glover, F.: Tabu search—part i. ORSA J. Comput. 1(3), 190–206 (1989)
Haas, W., Houghten, S.: A comparison of evolutionary algorithms for finding optimal error-correcting codes. In: Proceedings of the Third IASTED International Conference on Computational Intelligence, pp. 64–70. ACTA Press (2007)
Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Elsevier, Amsterdam (2004)
Nordstrom, A.W., Robinson, J.P.: An optimum nonlinear code. Inf. Control. 11(5-6), 613–616 (1967)
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Milshtein, M. A new two-error-correcting binary code of length 16. Cryptogr. Commun. 12, 71–75 (2020). https://doi.org/10.1007/s12095-019-00365-7
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DOI: https://doi.org/10.1007/s12095-019-00365-7