数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (2): 413-422.doi: 10.1016/S0252-9602(13)60008-9
刘修生
LIU Xiu-Sheng
摘要:
Let R be a finite chain ring with maximal ideal (γ) and residue field F, and let γ be of nilpotency index t. To every code C of length n over R, a tower of codes C = (C : γ0) ⊆ (C : γ) ⊆ … ⊆ (C : γi) ⊆ … ⊆ (C : γt−1) can be associated with C, where for any r ∈ R, (C : r) = {e ∈ Rn | re ∈ C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This
characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring.
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