Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 On norms, spread, characteristic polynomial and determinant of Hankel and Toeplitz matrices with Mersenne sequence 941 958 14876 10.22049/cco.2024.30037.2287 EN Kalika Prasad Department of Applied Science and Humanities (Mathematics), Government Engineering College Bhojpur, Bihar, India, 802301 0000-0002-3653-5854 Munesh Kumari Department of Applied Science and Humanities (Mathematics), Government Engineering College Bhojpur, Bihar, India, 802301 Jagmohan Tanti Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, India, 226025 0000-0002-0078-7494 Journal Article 2024 10 02 In this work, some new properties of the Hankel and Toeplitz matrices are obtained by considering the Mersenne numbers as entries. We developed efficient formulas to compute matrix norms like $\|.\|_1$,  $\|.\|_\infty$, Euclidean norm, spread, and the lower and upper bound for the spectral norm of these matrices. Also, the study shows that these matrices are non-singular for $n=2$ and singular for $n\geq 3$. Furthermore, we presented rank, eigenvalues, principal minors, and the characteristic polynomial of them explicitly. https://comb-opt.azaruniv.ac.ir/article_14876_e301d3063751d0a3d95c7843c5d4640b.pdf