Acta mathematica scientia, Series B >
ON THE CHARACTERIZATION OF CYCLIC CODES OVER TWO CLASSES OF RINGS
Received date: 2011-04-08
Revised date: 2012-07-08
Online published: 2013-03-20
Supported by
The author is supported by the Natural Science Foundation of Hubei Province (B20114410) and the Natural Science Foundation of Hubei Polytechnic University (12xjz14A).
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.
LIU Xiu-Sheng . ON THE CHARACTERIZATION OF CYCLIC CODES OVER TWO CLASSES OF RINGS[J]. Acta mathematica scientia, Series B, 2013 , 33(2) : 413 -422 . DOI: 10.1016/S0252-9602(13)60008-9
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