Constacyclic codes of length 2ps over Fpm+uFpmFpm+uFpm

The aim of this paper is to determine the algebraic structures of all λ  -constacyclic codes of length 2ps2ps over the finite commutative chain ring Fpm+uFpmFpm+uFpm, where p   is an odd prime and u2=0u2=0. For this purpose, the situation of λ is mainly divided into two cases separately. If the unit λ   is not a square and λ=α+uβλ=α+uβ for nonzero elements α,βα,β of FpmFpm, it is shown that the ambient ring (Fpm+uFpm)[x]/〈x2ps−(α+uβ)〉(Fpm+uFpm)[x]/〈x2ps−(α+uβ)〉 is a chain ring with the unique maximal ideal 〈x2−α0〉〈x2−α0〉, and thus (α+uβ)(α+uβ)-constacyclic codes are 〈(x2−α0)i〉〈(x2−α0)i〉 for 0≤i≤2ps0≤i≤2ps. If the unit λ   is not a square and λ=γλ=γ for some nonzero element γ   of FpmFpm, such λ-constacyclic codes are classified into 4 distinct types of ideals. The detailed structures of ideals in each type are provided. Among other results, the number of codewords and the dual of every λ-constacyclic code are obtained.