| Autor: |
Xuesong Si, Chuanze Niu |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 8, Iss 10, Pp 24434-24445 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20231246?viewType=HTML |
| Popis: |
The algebraic structure of skew cyclic codes over $ M_{2} $($ \mathbb{F}_2 $), using the $ \mathbb{F}_4 $-cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree $ d(x) $ is a free code generated by $ d(x) $. According to our findings, skew cyclic codes of odd and even lengths are cyclic and $ 2 $-quasi-cyclic over $ M_{2}(\mathbb{F}_{2}) $, respectively. We provide the self-dual skew condition of Hermitian dual codes of skew cyclic codes. The generator polynomials of Euclidean dual codes are obtained. Furthermore, a spanning set of a double skew cyclic code over $ M_{2}(\mathbb{F}_{2}) $ is considered in this paper. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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