4,580 research outputs found
Constructions of Batch Codes via Finite Geometry
A primitive -batch code encodes a string of length into string
of length , such that each multiset of symbols from has mutually
disjoint recovering sets from . We develop new explicit and random coding
constructions of linear primitive batch codes based on finite geometry. In some
parameter regimes, our proposed codes have lower redundancy than previously
known batch codes.Comment: 7 pages, 1 figure, 1 tabl
Mathematical LoRE: Local Recovery of Erasures using Polynomials, Curves, Surfaces, and Liftings
Employing underlying geometric and algebraic structures allows for
constructing bespoke codes for local recovery of erasures. We survey techniques
for enriching classical codes with additional machinery, such as using lines or
curves in projective space for local recovery sets or products of curves to
enhance the availability of data.Comment: IEEE BITS the Information Theory Magazine, to appea
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