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

Yongchao Wang, Yang Ding, Jiansheng Yang +1

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 sy…