The Number of Cycles of Bi-regular Tanner Graphs in Terms of the Eigenvalues of the Adjacency Matrix

arXiv:2601.05340v1 Announce Type: new
Abstract: In this paper, we explore new connections between the cycles in the graph of low-density parity-check (LDPC) codes and the eigenvalues of the corresponding adjacency matrix. The resulting observations are used to derive fast, simple, recursive formulas for the number of cycles $N_{2k}$ of length $2k$, $k