Stopping sets of codes from complete bipartite graph

Maimani, Hamidreza; Nazari, Mahbubeh; Tehranian, Abolfazl

doi:10.22061/jdma.2025.11781.1115

Stopping sets of codes from complete bipartite graph

Document Type : Full Length Article

Authors

¹ Department of Mathematics, Shahid Rajaee Teacher Training University

² Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran.

10.22061/jdma.2025.11781.1115

Abstract

Let $ C $ be a code with parity-check matrix $H$. A stopping set $S$ of size $ l\leq n $\index{$ l\leq n $} for $ H $ is an $ l $-columns submatrix of $ H_{s} $ of $ H $ which dose not contain a row with weight one. In this paper we consider the code which parity-check is incidence matrix of complete bipartite graph $K_{m,n}$. These codes are LDPC codes and we obtain the stopping sets for these codes.

Graphical Abstract