Repeated root cyclic FqFq-linear codes over FqlFql

Let FqFq be a finite field of cardinality q, where q is a power of a prime number p, n a positive multiple of p, l   a prime number and FqlFql an extension field of FqFq with degree l  . First, the structure and a canonical form decomposition of any cyclic FqFq-linear code over FplFpl of length n   are presented. Then from this decomposition and by the theory of linear codes over finite chain rings, enumeration, construction and encoder of these codes are investigated. Furthermore, the dual code of any cyclic FqFq-linear code over FplFpl of length n is studied.