All α+uβ-constacyclic codes of length np over Fpm+uFp

Repeated-Root Constacyclic Codes Over the Chain Ring Fpm[u]/⟨u3⟩

“…Using a technique different from that employed in [14], [15], [25], Cao et al [8] determined all α-constacyclic codes of length np s over F p m [v]/ v 2 and their dual codes by writing a canonical form decomposition for each code, where α is a non-zero element of F p m and n is a positive integer with gcd(p, n) = 1. In a recent work, Zhao et al [38] determined all (α + βv)-constacyclic codes of length np s over F p m [v]/ v 2 and their dual codes, where n is a positive integer coprime to p, and α, β are non-zero elements of F p m . This completely solved the problem of determination of all constacyclic codes of length np 2 and their dual codes, where n is a positive integer coprime to p. In a recent work [34], we determined all repeatedroot constacyclic codes of arbitrary lengths over the Galois ring GR(p 2 , m) of characteristic p 2 and cardinality p 2m , their sizes and their dual codes.…”