An integer programming model for obtaining cyclic quasi-difference matrices

Operations Research Perspectives - Tập 10 - Trang 100260 - 2023
Luis Martínez1, María Merino1,2, Juan Manuel Montoya1,3
1University of the Basque Country UPV/EHU, Department of Mathematics, 48080 Bilbao, Spain
2Basque Center for Applied Mathematics (BCAM), Alameda Mazarredo 14, 48009 Bilbo, Bizkaia, Spain
3University of Pamplona, Faculty of Basic Sciences, Pamplona, Colombia

Tài liệu tham khảo

Hedayat, 1999, Orthogonal arrays: Theory and applications 2007, Handbook of combinatorial designs Brouwer, 2012 Bose, 1961, On some connections between the design of experiments and information theory, Bull Inst Internat Statist, 38, 257 Delsarte, 1973, An algebraic approach to the association schemes of coding theory, Philips Res Rep Suppl, vi+97 Xu, 2021, A flexible image cipher based on orthogonal arrays, Inform Sci, 551, 39, 10.1016/j.ins.2020.11.029 Gopalakrishnan, 2006, Applications of orthogonal arrays to computer science, 149 Wang, 2008, Using orthogonal array to obtain gradient liquid chromatography conditions of enhanced peak intensity to determine geniposide and genipin with electrospray tandem mass spectrometry, J Chromatogr A, 1212, 68, 10.1016/j.chroma.2008.10.035 Taguchi, 1987 Goyeneche, 2014, Genuinely multipartite entangled states and orthogonal arrays, Phys Rev A, 90, 10.1103/PhysRevA.90.022316 Pang, 2019, Two and three-uniform states from irredundant orthogonal arrays, Npj Quant Inf, 5, 1 Dukanovic, 2007, Semidefinite programming relaxations for graph coloring and maximal clique problems, Math Program, 345, 10.1007/s10107-006-0026-z Seeger, 2014, Centers of sets with symmetry or cyclicity properties, TOP, 22, 716, 10.1007/s11750-013-0289-5 Buratti, 1999, Old and new designs via difference multisets and strong difference families, J Combin Des, 7, 406, 10.1002/(SICI)1520-6610(1999)7:6<406::AID-JCD2>3.0.CO;2-U Davis, 2016, Bi-cayley normal uniform multiplicative designs, Discrete Math, 339, 2224, 10.1016/j.disc.2016.03.028 Wilson, 1972, Cyclotomy and difference families in elementary abelian groups, J Number Theory, 4, 17, 10.1016/0022-314X(72)90009-1 Kutnar, 2009, Strongly regular tri-Cayley graphs, European J Combin, 30, 822, 10.1016/j.ejc.2008.09.002 Leung, 1993, Partial difference triples, J Algebraic Combin, 2, 397, 10.1023/A:1022475918250 Araluze, 2012, Partial sum quadruples and bi-Abelian digraphs, J Combin Theory Ser A, 119, 1811, 10.1016/j.jcta.2012.06.004 Araluze, 2011, Edge connectivity in difference graphs and some new constructions of partial sum families, European J Combin, 32, 352, 10.1016/j.ejc.2010.10.012 Bose, 1952, Orthogonal arrays of strength two and three, Ann Math Statist, 23, 508, 10.1214/aoms/1177729331 Abel, 2008, Some V(12,t) vectors and designs from difference and quasi-difference matrices, Australas J Combin, 40, 69 Wang, 2018, A short disproof of Euler’s conjecture based on quasi-difference matrices and difference matrices, Discrete Math, 341, 1114, 10.1016/j.disc.2017.10.019 Kutnar, 2013, Quasi m-Cayley strongly regular graphs, J Korean Math Soc, 50, 1199, 10.4134/JKMS.2013.50.6.1199 Radhakrishna Rao, 1947, Factorial experiments derivable from combinatorial arrangements of arrays, Suppl J R Statist Soc, 9, 128, 10.2307/2983576 Plackett, 1946, The design of optimum multifactorial experiments, Biometrika, 33, 305, 10.1093/biomet/33.4.305 Jungnickel, 1979, On difference matrices, resolvable transversal designs and generalized Hadamard matrices, Math Z, 167, 49, 10.1007/BF01215243 Ge, 2005, On (g,4;1)-difference matrices, Discrete Math, 301, 164, 10.1016/j.disc.2005.07.004 IBM ILOG Cplex, 2009, V12. 1: User’s manual for CPLEX, Int Bus Mach Corp, 46, 157 ARINA, 2021 The Sage Developers, 2020