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 $\mathbb{F}_q$.
[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. 18 (2024), no. 3, 661–673. https://doi.org/10.3934/amc.2022015
Karthick, G. (2025). Polycyclic codes over R. Communications in Combinatorics and Optimization, 10(2), 371-379. doi: 10.22049/cco.2023.28880.1760
MLA
Karthick, G. . "Polycyclic codes over R", Communications in Combinatorics and Optimization, 10, 2, 2025, 371-379. doi: 10.22049/cco.2023.28880.1760
HARVARD
Karthick, G. (2025). 'Polycyclic codes over R', Communications in Combinatorics and Optimization, 10(2), pp. 371-379. doi: 10.22049/cco.2023.28880.1760
CHICAGO
G. Karthick, "Polycyclic codes over R," Communications in Combinatorics and Optimization, 10 2 (2025): 371-379, doi: 10.22049/cco.2023.28880.1760
VANCOUVER
Karthick, G. Polycyclic codes over R. Communications in Combinatorics and Optimization, 2025; 10(2): 371-379. doi: 10.22049/cco.2023.28880.1760
)