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Binary codes from uniform subset graph G(n, 4, i) | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 11، شماره 3، آذر 2026، صفحه 235-246 اصل مقاله (347.31 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2026.12830.1183 | ||
| نویسندگان | ||
| Abolfazl Bahmani* 1؛ Mojgan Emami2 | ||
| 1Department of Mathematics, University of Zanjan Zanjan, Iran. | ||
| 2Department of Mathematics,University of Zanjan, Zanjan, Iran | ||
| تاریخ دریافت: 26 آذر 1404، تاریخ بازنگری: 14 مرداد 1405، تاریخ پذیرش: 23 مرداد 1405 | ||
| چکیده | ||
| Let Ω be a set of cardinality n with n ≥ 8, and let V = P4(Ω) denote the family of all 4-element subsets of Ω. For i = 0, 1, 2, 3, let G(n,4,i) be the graph with vertex set V, where two vertices are adjacent precisely when their intersection has cardinality i. This graph is referred to as the uniform subset graph. We denote the adjacency matrix of G(n,4,i) by Ai(n). In this work, we investigate the binary codes Ci(n) arising from the row space of Ai(n), determine their parameters, and establish the relationships between Ci(n) and Cj(n)⊥ for i,j ∈ {0,1,2,3}. | ||
| کلیدواژهها | ||
| binary codes؛ design؛ graphs؛ adjacency matrix | ||
| مراجع | ||
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[1] I. Anderson, Combinatorial Designs and Tournaments, Clarendon Press, Oxford, 1997. https://doi.org/10.1093/oso/9780198500292.001.0001 [2] A. Bahmani, M. Emami, O. Naserain, Dominating sets for uniform subset graphs, Linear Multilinear Algebra 72 (2024) 283–295. https://doi.org/10.1080/03081087.2022.2158295 [3] J. H. Castillo, L. D. Delgado-Ordonez, A. Holguin-Villa, Operations on binary linear codes and their associated graphs, arXiv preprint arXiv:2607.22800, (2026). https://doi.org/10.48550/arXiv.2607.22800 [4] W. Fish, Codes from Uniform Subset Graphs and Cyclic Products, PhD Thesis, University of the Western Cape, 2007. [5] R. Hill, A First Course in Coding Theory, Clarendon Press, Oxford, 1988. [6] J. D. Key, J. Moori, B. G. Rodrigues, Binary Codes from Graphs on Triples and Permutation Decoding, Ars Combin. 79 (2006) 11–19. [7] J. D. Key, J. Moori, B. G. Rodrigues, Binary Codes from Graphs on Triples, Discrete Math. 282(1-3) (2004) 171–182. https://doi.org/10.1016/j.disc.2003.12.004 [8] J. D. Key, J. Moori, B. G. Rodrigues, Ternary Codes from Graphs on Triples, Discrete Math. 309(14) (2009) 4663–4681. https://doi.org/10.1016/j.disc.2008.05.032 [9] J. C. Pang, H. Mahdavifar, S. S. Pradhan, New Bounds on the Size of Binary Codes With Large Minimum Distance, IEEE Journal on Selected Areas in Information Theory 4 (2023) 219–231. https://doi.org/10.1109/JSAIT.2023.3295836 | ||
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