Hensel's Lemma

Explicit Factorization of $x^{p+1}-1$ over $\mathbb{Z}_{p^e}$: A Structural Approach via Dickson Polynomials

arXiv:2604.19038v2 Announce Type: replace Abstract: Let $p$ be an odd prime. The factorization of the polynomial $x^{p+1}-1$ over the integer residue ring $\mathbb{Z}_{p^e}$ is pivotal for constructing cyclic codes with Hermitian symmetry, a critical resource for Linear Complementary Dual (LCD) codes and Entanglement-Assisted Quantum Error-Correcting Codes (EAQECC). Traditionally, lifting factorizations relies on the generic Hensel's Lemma, masking the underlying algebraic structure.