Search

The structure of λ -constacyclic codes of length 2 s over the Galois ring GR ( 2 a , m ) is obtained, for any unit λ of the form 4 z − 1 , z ∈ GR ( 2 a , m ) . The duals codes and necessary and sufficient conditions for the existence of a self-dual λ -constacyclic code are provided. Among others, this structure is used to establish the Hamming, homogeneous, and Rosenbloom–Tsfasman distances, and Rosenbloom–Tsfasman weight distribution of all such constacyclic codes. [ABSTRACT FROM AUTHOR]

Abstract: For any prime p, all constacyclic codes of length over the ring are considered. The units of the ring are of the forms γ and , where , and γ are nonzero elements of , which provides such constacyclic codes. First, the structure and Hamming distances of all constacyclic codes of length over the finite field are obtained; they are used as a tool to establish the structure and Hamming distances of all -constacyclic codes of length over . We then classify all cyclic codes of length over and obtain the number of codewords in each of those cyclic codes. Finally, a one-to-one correspondence between cyclic and γ-constacyclic codes of length over is constructed via ring isomorphism, which carries over the results regarding cyclic codes corresponding to γ-constacyclic codes of length over . [Copyright &y& Elsevier]