$\mathbb{F}_{p^{m}}\mathbb{F}_{p^{m}}{[u^2]}$-additive skew cyclic codes of length $2p^s $

Abstract

<p style='text-indent:20px;'>In this paper, we first study the skew cyclic codes of length <inline-formula><tex-math id="M3">\begin{document}$ p^s $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M4">\begin{document}$ R_3 = \mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}, $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M5">\begin{document}$ p $\end{document}</tex-math></inline-formula> is a prime number and <inline-formula><tex-math id="M6">\begin{document}$ u^3 = 0. $\end{document}</tex-math></inline-formula> Then we characterize the algebraic structure of <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{F}_{p^{m}}\mathbb{F}_{p^{m}}[u^2] $\end{document}</tex-math></inline-formula>-additive skew cyclic codes of length <inline-formula><tex-math id="M8">\begin{document}$ 2p^s. $\end{document}</tex-math></inline-formula> We will show that there are sixteen different types of these codes and classify them in terms of their generators.</p>

Comparative genomic analysis provides insights into the genetic diversity and pathogenicity of the genus Brucella

“…In addition, recent studies have revealed that the resistance of Brucella spp. to various antibiotics, such as rifampicin, Yang et al 10.3389/fmicb.2024.1389859 Frontiers in Microbiology 16 frontiersin.org azithromycin, tetracycline, and so on, has been increasing (Wareth et al, 2021(Wareth et al, , 2022Celik et al, 2023;Rezaei Shahrabi et al, 2023;Beig et al, 2024). These studies indicate an increase in antibiotic resistance in intracellular Brucella, which urgently requires attention.…”