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Stopping sets of codes from complete bipartite graph | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 11، شماره 2، شهریور 2026، صفحه 87-97 اصل مقاله (569.96 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.11781.1115 | ||
| نویسندگان | ||
| Hamidreza Maimani* 1؛ Mahbubeh Nazari2؛ Abolfazl Tehranian2 | ||
| 1Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Iran | ||
| 2Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran. | ||
| تاریخ دریافت: 05 اسفند 1403، تاریخ بازنگری: 21 اردیبهشت 1404، تاریخ پذیرش: 05 خرداد 1404 | ||
| چکیده | ||
| Let C be a code with parity-check matrix H. A stopping set S of size l ≤ n for H is an l-columns submatrix of Hs of H which does not contain a row with weight one. In this paper we consider the code which parity-check is incidence matrix of complete bipartite graph Km,n. These codes are LDPC codes and we obtain the stopping sets for these codes. | ||
| کلیدواژهها | ||
| linear code؛ stopping set؛ complete bipartite graph | ||
| مراجع | ||
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[1] P. Dankelmann, J. D. Key, B. G. Rodrigues, Codes from Incidence Matrices of Graphs, Univ. KwaZulu-Natal, Durban, 2011. [2] C. Di, D. Proietti, I. E. Telatar, T. J. Richardson, R. L. Urbanke, Finite-length analysis of low-density parity-check codes on the binary erasure channel, IEEE Trans. Inf. Theory 48 (2002) 1570–1579. [3] M. Esmaeili, A. Zaghian, On the combinatorial structure of a class of [(m,2),(m−1,2), 3] shortened Hamming codes and their dual codes, Discrete Appl. Math. 157 (2009) 356–363. [4] R. G. Gallager, Low-Density Parity-Check Codes, MIT Press, Cambridge, MA, 1963. [5] M. Nazari, H. R. Maimani, Stopping sets of codes from complete graph, J. Discrete Math. Sci. Cryptogr. 25 (2022) 1–10. [6] P. Solé, T. Zaslavsky, The covering radius of the cycle code of a graph, Discrete Appl. Math. 45 (1993) 63–70. [7] R. M. Tanner, A recursive approach to low complexity codes, IEEE Trans. Inf. Theory 27 (1981) 533–547. [8] A. Tucker, Applied Combinatorics, 4th ed., John Wiley & Sons, New York, 2002. [9] A. Velasquez, K. Subramani, P. Wojciechowski, On the complexity of and solutions to the minimum stopping and trapping set problems, Theoretical Computer Science 915 (2022) 26–44. | ||
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