The interplay of different metrics for the construction of constant dimension codes

<p style='text-indent:20px;'>A basic problem for constant dimension codes is to determine the maximum possible size <inline-formula><tex-math id="M1">\begin{document}$ A_q(n,d;k) $\end{document}</tex-math></inline-formula> of a set of <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-dimensional subspaces in <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_q^n $\end{document}</tex-math></inline-formula>, called codewords, such that the subspace distance satisfies <inline-formula><tex-math id="M4">\begin{document}$ d_S(U,W): = 2k-2\dim(U\cap W)\ge d $\end{document}</tex-math></inline-formula> for all pairs of different codewords <inline-formula><tex-math id="M5">\begin{document}$ U $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ W $\end{document}</tex-math></inline-formula>. Constant dimension codes have applications in e.g. random linear network coding, cryptography, and distributed storage. Bounds for <inline-formula><tex-math id="M7">\begin{document}$ A_q(n,d;k) $\end{document}</tex-math></inline-formula> are the topic of many recent research papers. Providing a general framework we survey many of the latest constructions and show the potential for further improvements. As examples we give improved constructions for the cases <inline-formula><tex-math id="M8">\begin{document}$ A_q(10,4;5) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M9">\begin{document}$ A_q(11,4;4) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ A_q(12,6;6) $\end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id="M11">\begin{document}$ A_q(15,4;4) $\end{document}</tex-math></inline-formula>. We also derive general upper bounds for subcodes arising in those constructions.</p>

Enhanced packet reordering procedure to improve TCP communication

Purpose The research work is attained by Spurious Transmission–based Enhanced Packet Reordering Method (ST-EPRM). The packet reordering necessity is evaded by presenting random linear network coding process on wireless network physical layer which function on basis of sequence numbers. The spurious retransmission happening over wireless network is obtained by presenting monitoring concept for reducing number of spurious retransmissions because it might need more than three DUPACKs for triggering fast retransmit. This monitoring node performs as centralized node as well variation amid buffer length and number of packets being sent can be predicted. This information helps in differentiating spurious retransmission from the packet loss. Design/methodology/approach Based on transmission detection, action is accomplished whether to retransmit or evade transmission. Monitoring node selection is achieved by presenting improved cuckoo search algorithm. The modified support vector machine algorithm is greatly used for variation-based spurious transmission. Findings The research work which is attained by ST-EPRM. The packet reordering necessity is evaded by presenting random linear network coding process on wireless network physical layer which function on basis of sequence numbers. The spurious retransmission happening over wireless network is obtained by presenting monitoring concept for reducing number of spurious retransmissions because it might need more than three DUPACKs for triggering fast retransmit. This monitoring node performs as centralized node as well variation amid buffer length and number of packets being sent can be predicted. This information helps in differentiating spurious retransmission from the packet loss. Originality/value Based on transmission detection, action is accomplished whether to retransmit or evade transmission. Monitoring node selection is achieved by presenting improved cuckoo search algorithm. The modified support vector machine algorithm is greatly used for variation-based spurious transmission.