Simple-Root cyclic and negacyclic codes over finite chain rings
Keywords
Cyclic codes, negacyclic codes, constacyclic codes, simple root, dual codes, codes over finite rings, Hamming distance, homogeneous distance, Lee distance,
Abstract
This paper provides an overview of results related to simple-root cyclic and negacyclic codes over finite commutative chain rings. Algebraic structures of all such codes and their duals are established. Necessary and sufficient conditions for self-dual codes are discussed. In particular, several situations are presented for the nonexistence of nontrivial self-dual codes.
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