Structure of codes over the ring Z_{3}[v]/langle v^{3}-vrangle |
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Authors: | Aysegul Bayram Irfan Siap |
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Affiliation: | 1. Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University, Istanbul, Turkey
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Abstract: | In this paper, we study the structure of linear codes over the non chain ring $Z_{3}[v]/langle v^{3}-vrangle $ . In order to study the codes, we first study the structure of this ring via a distance preserving Gray map which also induces a relation between codes over this ring and ternary codes. Further, the algebraic structure of cyclic and dual codes is also studied. A MacWilliams type Identity between the Gray weight enumerators of the original code and its dual is established. In all cases examples that illustrate the theorems and lemmas are provided. Also, a BCH-type bound and an example that attains this bound is presented. |
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