Correcting adversarial errors with generalized regenerating codes

<p style='text-indent:20px;'>Traditional regenerating codes are efficient tools to optimize both storage and repair bandwidth in storing data across a distributed system, particularly comparison erasure replication. In traditional codes, the collection of any <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math></inline-formula> nodes can reconstruct all stored information is called reconstruction set, id="M2">\begin{document}$ \aleph _R $\end{document}</tex-math></inline-formula>. A failed node be regenerated from id="M3">\begin{document}$ d surviving nodes. These collections id="M4">\begin{document}$ regeneration sets, id="M5">\begin{document}$ _H The number sets satisfy id="M6">\begin{document}$ |\aleph _R| = C_n^k id="M7">\begin{document}$ _H| C_{n-1}^d generalized we will have, id="M8">\begin{document}$ 1\le|\aleph_R|\le C^k_n id="M9">\begin{document}$ 1\le|\aleph_H|\le this paper, address problem secure present coding scheme by focusing on features that protects system presence an active omniscient adversary. This adversary maliciously alter under its control send erroneous outgoing message when contacted for our notwithstanding collector still obtain original file using classical minimum distance decoder.</p>