Polycyclic codes over [formula omitted]: Classification, Hamming distance, and annihilators

Abstract

Let p be prime integer, s and m positive integers; f(x) be a monic irreducible polynomial over R where R:=Fpm[u]/〈u2〉. This paper gives a complete classification of polycyclic codes over R associated to f(x)ps, and the other hand, when f(x)∈Fpm[x], their Hamming distances and their annihilators are explicitly given.