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Linear and cyclic codes over direct product of finite chain rings
Author(s) -
Borges J.,
FernándezCórdoba C.,
TenValls R.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4491
Subject(s) - mathematics , chain (unit) , direct product , product (mathematics) , polynomial ring , discrete mathematics , generator matrix , duality (order theory) , generator (circuit theory) , linear code , cyclic code , polynomial code , pure mathematics , combinatorics , polynomial , block code , algorithm , mathematical analysis , decoding methods , power (physics) , physics , geometry , astronomy , quantum mechanics
We introduce a new type of linear and cyclic codes. These codes are defined over a direct product of 2 finite chain rings. The definition of these codes as certain submodules of the direct product of copies of these rings is given, and the cyclic property is defined. Cyclic codes can be seen as submodules of the direct product of polynomial rings. Generator matrices for linear codes and generator polynomials for cyclic codes are determined. Further, we study the concept of duality.