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A265032
Maximal size of an error-correcting code of length n and minimal distance 3 over an alphabet of size 4.
9
1, 1, 4, 16, 64
OFFSET
1,3
COMMENTS
The alphabet may be any set of size 4 (GF(4), Z/4Z, etc.) so there is no requirement of linearity.
a(6) is known to be in the range [164-179], and a(7) in the range [512-614].
LINKS
R. Barden, N. Bushaw, C. Callison, A. Fernandez, B. Harris, I. Holden, C. E. Larson, D. Muncy, C. O'Shea, J. Shive, J. Raines, P. Rana, N. van Cleemput, B. Ward, and N. Wilcox-Cook, The Graph Brain Project & Big Mathematics, research paper, 2017.
Galina T. Bogdanova, Andries E. Brouwer, Stoian N. Kapralov, and Patric R. J. Östergård, Error-Correcting Codes over an Alphabet of Four Elements, Designs, Codes and Cryptography 23 (2001) 333-342.
Maryam Fazel and Omid Sadeghi, Fast First-Order Methods for Monotone Strongly DR-Submodular Maximization, Proc. SIAM Conf. Appl. Comp. Disc. Algo. (ACDA23, 2023), 169-179. See page 178.
Balázs Király and Sándor Szabó, Splitting Edge Partitions of Graphs, Mathematica Pannonica (2023).
Christopher Hojny, Marc E. Pfetsch, and José Verschae, The Impact of Symmetry Handling for the Stable Set Problem via Schreier-Sims Cuts, arXiv:2311.06085 [math.OC], 2023.
Raffaele Marino, Lorenzo Buffoni, and Bogdan Zavalnij, A Short Review on Novel Approaches for Maximum Clique Problem: from Classical algorithms to Graph Neural Networks and Quantum algorithms, arXiv:2403.09742 [cs.AI], 2024. See index p. 36.
Pablo San Segundo, Fabio Furini, and Jorge Artieda, A new branch-and-bound algorithm for the Maximum Weighted Clique Problem, Computers & Operations Research (2019) Vol. 110, 18-33.
Sándor Szabó, Estimating the fractional chromatic number of a graph, Acta Univ. Sapientiae Informatica (2021) Vol. 13, No. 1, 122-133.
Sándor Szabó and Bogdán Zaválnij, Estimating clique size via discarding subgraphs, Informatica (2021) Vol. 45, 197-204.
Sándor Szabó and Bogdán Zaválnij, Solving hard optimization problems of packing, covering, and tiling via clique search, 27th Info. Soc. Multiconf. (2024).
Boglárka Gazdag-Tóth, Eligius María Theodorus Hendrix, and Leocadio González Casado, On monotonicity and search strategies in face-based copositivity detection algorithms, Cent Eur J Oper Res (2021).
Chuixiong Wu, Jianan Wang, and Fen Zuo, From Maximum Cut to Maximum Independent Set, arXiv:2408.06758 [quant-ph], 2024. See references.
Oleksandra Yezerska and Sergiy Butenko, The Maximum Clique and Vertex Coloring, Handbook of Heuristics. Springer, Cham, 2018, 1-31.
Bogdán Zaválnij, The k-Clique Problem--Usage, Modeling Expressivity, Serial and Massively Parallel Algorithms, Ph. D. Dissertation, University of Szeged (Hungary, 2020).
CROSSREFS
Sequence in context: A282310 A022030 A135450 * A162547 A073533 A330689
KEYWORD
nonn,more,changed
AUTHOR
N. J. A. Sloane, Dec 05 2015
STATUS
approved