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Polycyclic codes over R | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 آذر 1402 اصل مقاله (381.21 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28880.1760 | ||
| نویسنده | ||
| Gowdhaman Karthick* | ||
| Mathematics, Presidency University, Banglore, Karnataka, India | ||
| چکیده | ||
| In this paper, we discuss the structure of polycyclic codes over the ring $R=\mathbb{F}_q+u\mathbb{F}_q+v\mathbb{F}_q;u^2=\alpha u,v^2=v$ and $uv=vu=0$, where $\alpha$ is an unit element in $R.$ We introduce annihilator self-dual codes, annihilator self-orthogonal codes and annihilator LCD codes over R. Using a Gray map, we define a one to one correspondence between $R$ and $\mathbb{F}_q$ and construct quasi polycyclic codes over the $\mathbb{F}_q$. | ||
| کلیدواژه‌ها | ||
| Semi-simple ring؛ polycyclic codes؛ Hamming distances؛ Gray maps؛ annihilator dual codes | ||
| مراجع | ||
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[1] A. Alahmadi, S.T. Dougherty, A. Leroy, and P. Solé, On the duality and the direction of polycyclic codes, Adv. Math. Commun. 10 (2016), no. 4, 921–929. https://doi.org/10.3934/amc.2016049 [2] A. Fotue-Tabue, E. MartÍnez-Moro, and J.T. Blackford, On polycyclic codes over a finite chain ring., Adv. Math. Commun. 14 (2020), no. 3, 455–466. https://doi.org/10.3934/amc.2020028 [3] S.R. López-Permouth, B.R. Parra-Avila, and S. Szabo, Dual generalizations of the concept of cyclicity of codes., Adv. Math. Commun. 3 (2009), no. 3, 227–234. https://doi.org/10.3934/amc.2009.3.227 [4] W. Qi, On the polycyclic codes over $\mathbb F_q + u\mathbb F_q$, Adv. Math. Commun. (In press),
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