4,580 research outputs found

    Constructions of Batch Codes via Finite Geometry

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    A primitive kk-batch code encodes a string xx of length nn into string yy of length NN, such that each multiset of kk symbols from xx has kk mutually disjoint recovering sets from yy. 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

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    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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