the *generalized fractional repetition* code, which can be viewed as a generalization of the existing fractional repetition codes [@el2010fractional].

The rest of this paper is organized as follows. Section \[sec:prob\_stat\] motivates the problem and introduces key definitions and notation. Section \[sec:comparison\] compares our setup to existing code setups. Section \[sec:preview\] gives a preview of our main results in this paper. Section \[sec:results\] states the main results of this paper. Section \[sec:converse\] states and proves the converse part of our main results. Section \[sec:achievability\] states and proves the achievability part by proposing the FHS scheme and its extension and analyzing their performance. Section \[sec:conc\] concludes this paper.

Problem Statement {#sec:prob_stat}
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The Parameters of a Distributed Storage Network
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[**Parameters $n$ and $k$:**]{} We denote the total number of nodes in a storage network by $n$. For any $1\leq k\leq n-1$, we say that a code can satisfy the reconstruction requirement if any $k$ nodes can be used to reconstruct the original data/file. For example, consider a network of 7 nodes. A $(7,4)$ Hamming code can be used to protect the data. We say that the Hamming code can satisfy the reconstruction requirement for $k=6$. Specifically, any 6 nodes can construct 