Construction of storage codes of rate approaching one on triangle-free graphs
H Huang, Q Xiang - Designs, Codes and Cryptography, 2023 - Springer
Consider an assignment of bits to the vertices of a connected graph Γ (V, E) with the property
that the value of each vertex is a function of the values of its neighbors. A collection of such …
that the value of each vertex is a function of the values of its neighbors. A collection of such …
Nearly orthogonal sets over finite fields
D Chawin, I Haviv - arXiv preprint arXiv:2402.08274, 2024 - arxiv.org
For a field $\mathbb {F} $ and integers $ d $ and $ k $, a set of vectors of $\mathbb {F}^ d $ is
called $ k $-nearly orthogonal if its members are non-self-orthogonal and every $ k+ 1$ of …
called $ k $-nearly orthogonal if its members are non-self-orthogonal and every $ k+ 1$ of …
The BCH Family of Storage Codes on Triangle-Free Graphs is of Unit Rate
H Deng, H Huang, G Weng, Q Xiang - arXiv preprint arXiv:2310.04820, 2023 - arxiv.org
Let $\Gamma $ be a simple connected graph on $ n $ vertices, and let $ C $ be a code of
length $ n $ whose coordinates are indexed by the vertices of $\Gamma $. We say that $ C …
length $ n $ whose coordinates are indexed by the vertices of $\Gamma $. We say that $ C …
Optimal storage codes on graphs with fixed locality
S Basu, M Mukherjee - arXiv preprint arXiv:2307.08680, 2023 - arxiv.org
Storage codes on graphs are an instance of\emph {codes with locality}, which are used in
distributed storage schemes to provide local repairability. Specifically, the nodes of the …
distributed storage schemes to provide local repairability. Specifically, the nodes of the …
Storage codes on coset graphs with asymptotically unit rate
A storage code on a graph $ G $ is a set of assignments of symbols to the vertices such that
every vertex can recover its value by looking at its neighbors. We consider the question of …
every vertex can recover its value by looking at its neighbors. We consider the question of …
Recoverable systems
O Elishco, A Barg - IEEE transactions on information theory, 2022 - ieeexplore.ieee.org
Motivated by the established notion of storage codes, we consider sets of infinite sequences
over a finite alphabet such that every-tuple of consecutive entries is uniquely recoverable …
over a finite alphabet such that every-tuple of consecutive entries is uniquely recoverable …
The BCH Family of Storage Codes on Triangle-Free Graphs and Its Relation to R(3, t)
H Deng, H Huang, G Weng… - IEEE Transactions on …, 2024 - ieeexplore.ieee.org
Consider a simple, connected graph Γ with n vertices. Let C be a code of length n with its
coordinates corresponding to the vertices of Γ. We define C as a storage code on Γ if, for any …
coordinates corresponding to the vertices of Γ. We define C as a storage code on Γ if, for any …
Storage codes and recoverable systems on lines and grids
A storage code is an assignment of symbols to the vertices of a connected graph $ G (V, E) $
with the property that the value of each vertex is a function of the values of its neighbors, or …
with the property that the value of each vertex is a function of the values of its neighbors, or …
On extremal rates of storage over graphs
A storage code over a graph maps independent source symbols, each of bits, to coded
symbols, each of bits, such that each coded symbol is stored in a node of the graph and …
symbols, each of bits, such that each coded symbol is stored in a node of the graph and …
Recoverable systems on lines and grids
A storage code is an assignment of symbols to the vertices of a connected graph G (V, E)
with the property that the value of each vertex is a function of the values of its neighbors, or …
with the property that the value of each vertex is a function of the values of its neighbors, or …