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Good asymptotic behavior of additive cyclic codes on $ \mathbb{F}_{q}[u]/ \langle u^{2} \rangle \times \mathbb{F}_{q}[u]/ \langle u^{3} \rangle $ | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 فروردین 1405 اصل مقاله (207.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.30109.1780 | ||
| نویسندگان | ||
| A. Isapour-khsadan1؛ Sh. Mehry* 2؛ S. Mahmoudi3 | ||
| 1Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran Faculty of Basic Sciences, Khatam-ol-Anbia(PBU) University, Tehran, Iran | ||
| 2Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran | ||
| 3Department of Mathematics, Bu Ali Sina University, Hamedan, Iran | ||
| چکیده | ||
| Let $ S= \mathbb{F}_{q}[u]/ \langle u^2\rangle$ = $ \mathbb{F}_{q}+u\mathbb{F}_{q}$ and $R=\mathbb{F}_{q}[u]/ \langle u^3\rangle$ = $\mathbb{F}_{q}+u\mathbb{F}_{q} + u^{2}\mathbb{F}_{q}$ are two finite chain rings, where $ u^{2}=0=u^{3} $ and $ q $ is a power of a prime number. We construct a class of $ SR $-additive cyclic codes generated by pairs of polynomials, where $ S $ is a $ R $-algebra and $ SR $-additive cyclic code is a $ R $-submodul of $ S^{\alpha} \times R^{\beta} $ . Based on probabilistic arguments, we study the asymptotic behaviour of the rates and relative minimum distances of a certain class of the codes. We show that there exists an asymptotically good infinite seqence of $ SR $-additive cyclic codes with the relative minimum distance of the code is convergent to $ \delta $, and the rat is convergent to $ \frac{2}{q+q^{2}} $ for $ 0 < \delta < \frac{1}{1+q} $. | ||
| کلیدواژهها | ||
| $ \mathbb{F}_{q}[u]/ \langle u^2\rangle \times \mathbb{F}_{q}[u]/\langle u^3 \rangle $ -Additive cyclic codes؛ Random codes؛ Asymptotically good؛ Cumulative weight enumerator | ||
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آمار تعداد مشاهده مقاله: 2 تعداد دریافت فایل اصل مقاله: 2 |
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