You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Additive cyclic codes over Galois rings were investigated in previous works. In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the previous studies, whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples.

Cited Abstract(s):
[1]: Let R = GR ( p ? , l ) be a Galois ring of characteristic p ? and cardinality p ? l , where p and l are prime integers. First, we give a canonical form decomposition for additive cyclic codes over R . This decomposition is used to construct additive cyclic codes and count the number of such codes, respectively. Then we give the trace dual code for each additive cyclic code over R from its canonical form decomposition and linear codes of length l over some extension Galois rings of Z p ? .
Additive cyclic codes over Galois rings were investigated in [1] . In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity.