Cyclic codes over $${\mathcal {M}}_4({\mathbb {F}}_2$$ M 4 ( F 2 )
| العنوان: | Cyclic codes over $${\mathcal {M}}_4({\mathbb {F}}_2$$ M 4 ( F 2 ) |
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| المؤلفون: | Joydeb Pal, Satya Bagchi, Sanjit Bhowmick |
| المصدر: | Journal of Applied Mathematics and Computing. 60:749-756 |
| بيانات النشر: | Springer Science and Business Media LLC, 2019. |
| سنة النشر: | 2019 |
| مصطلحات موضوعية: | Ring (mathematics), Applied Mathematics, Image (category theory), 020206 networking & telecommunications, Field (mathematics), 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Combinatorics, Computational Mathematics, Gray map, 010201 computation theory & mathematics, Cyclic code, 0202 electrical engineering, electronic engineering, information engineering, Mathematics |
| الوصف: | In this article, keeping the huge research prospective of the study in mind, we consider the non-commutative ring $${\mathcal {M}}_4({\mathbb {F}}_2)$$ , the set of all $$4 \times 4$$ matrices over the field $${\mathbb {F}}_2$$ and confirm that this ring is isomorphic with the ring $${\mathbb {F}}_{16}+u {\mathbb {F}}_{16}+u^2 {\mathbb {F}}_{16}+u^3{\mathbb {F}}_{16}$$ , where $$u^4=0$$ . Besides, we develop the structure of cyclic codes and their generators over the ring. Also, making use of Gray map from $${\mathcal {M}}_4({\mathbb {F}}_2)$$ to $${\mathbb {F}}_{16}^4$$ , we infer that the image of a cyclic code is a linear code. Finally, our findings are authenticated by suitable non-trivial examples. |
| تدمد: | 1865-2085 1598-5865 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::13670e04beb9dbfa02eb11962e50cd4e https://doi.org/10.1007/s12190-018-01235-w |
| حقوق: | CLOSED |
| رقم الأكسشن: | edsair.doi...........13670e04beb9dbfa02eb11962e50cd4e |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 18652085 15985865 |
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