Algebraic hierarchical locally recoverable codes with nested affine subspace recovery

Algebraic hierarchical locally recoverable codes with nested affine subspace recovery

Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. Theses subsets are typically of small cardinality to promote recovery using limited network traffic and other resources. Hierarchical locally recoverable codes allo...

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Hauptverfasser: Haymaker, Kathryn, Malmskog, Beth, Matthews, Gretchen L
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Computer Science - Information Theory
Mathematics - Algebraic Geometry
Mathematics - Information Theory
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description Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. Theses subsets are typically of small cardinality to promote recovery using limited network traffic and other resources. Hierarchical locally recoverable codes allow for recovery of erasures using sets of other symbols whose sizes increase as needed to allow for recovery of more symbols. In this paper, we construct codes with hierarchical locality from a geometric perspective, using fiber products of curves. We demonstrate how the constructed hierarchical codes can be viewed as punctured subcodes of Reed-Muller codes. This point of view provides natural structures for local recovery at each level in the hierarchy.
doi_str_mv 10.48550/arxiv.2310.20533
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Mathematics - Information Theory
title Algebraic hierarchical locally recoverable codes with nested affine subspace recovery
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