On negacyclic codes of length \(5p^s\) over \(\mathbb{F}_{p^m}+u \mathbb{F}_{p^m}\)
Brahim Boudine, Jamal Laaouine, Hamid Ben Yakkou · Journal of Combinatorial Mathematics and Combinatorial Computing · 2025
Let \(p > 5\) be a prime positive integer, \(m\) and \(s\) be positive integers. We classify the negacyclic codes of length \(5p^s\) over \(R= \mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\), with \(u^2=0\) using the factorisation of cyclotomic polynomials, and we investigate their Hamming distances.