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TitleCodes over finite quotients of polynomial rings
Author(s) Nora El Amrani, Thierry P. Berger
TypeArticle in Journal
AbstractAbstract In this paper, we study codes that are defined over the polynomial ring A = F [ x ] / f ( x ) , where f ( x ) is a monic polynomial over a finite field F . We are interested in codes that are A -submodules of A ℓ . These codes are a generalization of quasi-cyclic codes. In this work we introduce a notion of basis of divisors for these codes and a canonical generator matrix. It is a generalization of the work of K. Lally and P. Fitzpatrick. However, in contrast with K. Lally and P. Fitzpatrick, we do not use the Gröbner basis, but only the classical Euclidean division. We also study the notion of A -duality and the link with the q-ary images of these codes and the F -duality.
KeywordsCyclic codes, Quasi-cyclic codes, Polynomial ring, q-ary image, Duality
URL http://www.sciencedirect.com/science/article/pii/S1071579713001020
JournalFinite Fields and Their Applications
Pages165 - 181
Translation No
Refereed No