Balaji Srinivasan Babu, Ganesh Ramachandra Kini, P. V. Kumar
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A Rate-Optimal Construction of Codes with Sequential Recovery with Low Block Length
An erasure code is said to be a code with sequential recovery with parameters $r$ and t, if for any $s$ ≤ $t$ erased code symbols, there is an s-step recovery process in which at each step we recover exactly one erased code symbol by contacting at most $r$ other code symbols. In this paper, we give a construction of binary codes with sequential recovery that are rate-optimal for any value of $t$ and any value $r$ ≥ 3. Our construction is based on construction of certain kind of tree-like graphs with girth $t$ + 1. We construct these graphs and hence the codes recursively.
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