On negacyclic codes of length \(5p^s\) over \(\mathbb{F}_{p^m}+u \mathbb{F}_{p^m}\)

<p>Let <span class="math inline">\(p > 5\)</span> be a prime positive integer, <span class="math inline">\(m\)</span> and <span class="math inline">\(s\)</span> be positive integers. We classify the negacyclic codes of length <span class="math inline">\(5p^s\)</span> over <span class="math inline">\(R= \mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\)</span>, with <span class="math inline">\(u^2=0\)</span> using the factorisation of cyclotomic polynomials, and we investigate their Hamming distances.</p>