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Maximal size of an error-correcting code of length n and minimal distance 3 over an alphabet of size 4.
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%I #85 Oct 02 2024 04:23:54

%S 1,1,4,16,64

%N Maximal size of an error-correcting code of length n and minimal distance 3 over an alphabet of size 4.

%C The alphabet may be any set of size 4 (GF(4), Z/4Z, etc.) so there is no requirement of linearity.

%C a(6) is known to be in the range [164-179], and a(7) in the range [512-614].

%H N. J. A. Sloane, <a href="/A265032/a265032.html">Challenge Problems: Independent Sets in Graphs</a>

%H 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, <a href="http://www.people.vcu.edu/~clarson/AC7-GBP-171019.pdf">The Graph Brain Project & Big Mathematics</a>, research paper, 2017.

%H Galina T. Bogdanova, Andries E. Brouwer, Stoian N. Kapralov, and Patric R. J. Östergård, <a href="https://doi.org/10.1023/A:1011275112159">Error-Correcting Codes over an Alphabet of Four Elements</a>, Designs, Codes and Cryptography 23 (2001) 333-342.

%H Maryam Fazel and Omid Sadeghi, <a href="https://doi.org/10.1137/1.9781611977714.15">Fast First-Order Methods for Monotone Strongly DR-Submodular Maximization</a>, Proc. SIAM Conf. Appl. Comp. Disc. Algo. (ACDA23, 2023), 169-179. See page 178.

%H Balázs Király and Sándor Szabó, <a href="https://doi.org/10.1556/314.2023.00002">Splitting Edge Partitions of Graphs</a>, Mathematica Pannonica (2023).

%H Christopher Hojny, Marc E. Pfetsch, and José Verschae, <a href="https://arxiv.org/abs/2311.06085">The Impact of Symmetry Handling for the Stable Set Problem via Schreier-Sims Cuts</a>, arXiv:2311.06085 [math.OC], 2023.

%H Prabhu Manyem, <a href="https://www.researchgate.net/publication/380034972_Maximum_independent_set_stable_set_problem_A_Satisfiability_SAT_based_model_and_Computational_testing">Maximum independent set (stable set) problem: A Satisfiability (3SAT) based model and Computational testing</a>, ResearchGate, 2024. See pp. 4, 8.

%H Raffaele Marino, Lorenzo Buffoni, and Bogdan Zavalnij, <a href="https://arxiv.org/abs/2403.09742">A Short Review on Novel Approaches for Maximum Clique Problem: from Classical algorithms to Graph Neural Networks and Quantum algorithms</a>, arXiv:2403.09742 [cs.AI], 2024. See index p. 36.

%H Albert No, <a href="https://doi.org/10.3390/e21121202">Nonasymptotic Upper Bounds on Binary Single Deletion Codes via Mixed Integer Linear Programming</a>, Entropy (2019) Vol. 21, 1202.

%H Pablo San Segundo, Fabio Furini, and Jorge Artieda, <a href="https://doi.org/10.1016/j.cor.2019.05.017">A new branch-and-bound algorithm for the Maximum Weighted Clique Problem</a>, Computers & Operations Research (2019) Vol. 110, 18-33.

%H Sándor Szabó, <a href="https://doi.org/10.2478/ausi-2021-0006">Estimating the fractional chromatic number of a graph</a>, Acta Univ. Sapientiae Informatica (2021) Vol. 13, No. 1, 122-133.

%H Sándor Szabó and Bogdán Zaválnij, <a href="https://doi.org/10.31449/inf.v45i2.3107">Estimating clique size via discarding subgraphs</a>, Informatica (2021) Vol. 45, 197-204.

%H Sándor Szabó and Bogdán Zaválnij, <a href="https://is.ijs.si/wp-content/uploads/2024/09/IS2024_-_SIKDD_2024_paper_9.pdf">Solving hard optimization problems of packing, covering, and tiling via clique search</a>, 27th Info. Soc. Multiconf. (2024).

%H Boglárka Gazdag-Tóth, Eligius María Theodorus Hendrix, and Leocadio González Casado, <a href="https://doi.org/10.1007/s10100-021-00737-6">On monotonicity and search strategies in face-based copositivity detection algorithms</a>, Cent Eur J Oper Res (2021).

%H Chuixiong Wu, Jianan Wang, and Fen Zuo, <a href="https://arxiv.org/abs/2408.06758">From Maximum Cut to Maximum Independent Set</a>, arXiv:2408.06758 [quant-ph], 2024. See references.

%H Oleksandra Yezerska and Sergiy Butenko, <a href="https://doi.org/10.1007/978-3-319-07153-4_47-1">The Maximum Clique and Vertex Coloring</a>, Handbook of Heuristics. Springer, Cham, 2018, 1-31.

%H Bogdán Zaválnij, <a href="http://doktori.bibl.u-szeged.hu/10444/1/diss-beadott.pdf">The k-Clique Problem--Usage, Modeling Expressivity, Serial and Massively Parallel Algorithms</a>, Ph. D. Dissertation, University of Szeged (Hungary, 2020).

%K nonn,more

%O 1,3

%A _N. J. A. Sloane_, Dec 05 2015