Self-Dual Double Circulant, Self-Dual Double Negacirculant and LCD Double Negacirculant Codes Over the Ring Fq[u,v]/2 - u, v2-v, uv-vu>
In: IEEE Access, Jg. 11 (2023), S. 92898-92912
Online
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Zugriff:
In this paper, we investigate self-dual double circulant, and self-dual and linear complementary dual (LCD) double negacirculant codes over a finite ring $R = \mathbb F_{q} + u \mathbb F_{q} + v \mathbb F_{q} + uv\mathbb F_{q}$ , where $u^{2}=u$ , $v^{2}=v$ , $uv=vu $ and $q=p^{m}$ . We study the algebraic structure of double circulant codes over $R$ . We provide necessary and sufficient conditions for a double circulant code to be a self-dual code. We give a formula to get the total number of self-dual double circulant codes over the ring $R$ . We compute distance bounds for self-dual double circulant codes over $R$ . In addition, by using a Gray map, we show that the families of self-dual double circulant codes under the Gray map are asymptotically good. Moreover, the algebraic structure of double negacirculant codes and necessary and sufficient conditions for a double negacirculant code to be a self-dual code and to be an LCD code are also given. We determine the total number of self-dual and LCD double negacirculant codes over $R$ .
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Self-Dual Double Circulant, Self-Dual Double Negacirculant and LCD Double Negacirculant Codes Over the Ring Fq[u,v]/2 - u, v2-v, uv-vu>
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Autor/in / Beteiligte Person: | Dinh, Hai Q. ; Bhanu Pratap Yadav ; Nguyen, Bac T. ; Ashish Kumar Upadhyay ; Yamaka, Woraphon |
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Zeitschrift: | IEEE Access, Jg. 11 (2023), S. 92898-92912 |
Veröffentlichung: | IEEE, 2023 |
Medientyp: | academicJournal |
ISSN: | 2169-3536 (print) |
DOI: | 10.1109/ACCESS.2023.3309246 |
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