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Repeated-root cyclic and negacyclic codes over a finite chain ring [PDF]

open access: yesDiscrete Applied Mathematics, 2006
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2.
Ana Sàlàgean
exaly   +9 more sources

On the Structure of Linear and Cyclic Codes over a Finite Chain Ring

Applicable Algebra in Engineering, Communications and Computing, 2000
In [\textit{A. R. Calderbank} and \textit{N. J. A. Sloane}, Des. Codes Cryptography 6, 21-35 (1995; Zbl 0848.94020)], structure theorems are given for linear and cyclic codes over \(\mathbb{Z}_{p^a}\). Such codes received much attention after the discovery that important families of binary nonlinear codes can be obtained as images under a Gray mapping ...
Ana Sàlàgean
exaly   +3 more sources

Cyclic and Negacyclic Codes Over Finite Chain Rings

IEEE Transactions on Information Theory, 2004
The structures of cyclic and negacyclic codes of length n and their duals over a finite chain ring R are established when n is not divisible by the characteristic of the residue field R~. Some cases where n is divisible by the characteristic of the residue field R~ are also considered.
Hai Quang Dinh 0001   +1 more
exaly   +3 more sources

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