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Creators/Authors contains: "Malmskog, Beth"

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  1. ; ; (, Journal of Algebra and Its Applications)
    In this paper, we construct codes with hierarchical locality using natural geometric structures in Artin–Schreier surfaces of the form [Formula: see text]. Our main theorem describes the codes, their hierarchical structure and recovery algorithms, and gives parameters. We also develop a family of examples using codes defined over [Formula: see text] on the surface [Formula: see text]. We use elementary methods to count the [Formula: see text]-rational points on the surface, enabling us to provide explicit hierarchical parameters and a better bound on minimum distance for these codes. An additional example and some generalizations are also considered. 
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    Free, publicly-accessible full text available December 1, 2026
  2. ; (, Involve, a Journal of Mathematics)
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  3. ; ; (, Designs, Codes and Cryptography)
    Abstract Codes with locality, also known as locally recoverable codes, allow for recovery of erasures using proper subsets of other coordinates. These 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 describe a hierarchical recovery structure arising from geometry in Reed–Muller codes and codes with availability from fiber products of curves. We demonstrate how the fiber product hierarchical codes can be viewed as punctured subcodes of Reed–Muller codes, uniting the two constructions. This point of view provides natural structures for local recovery with availability at each level in the hierarchy. 
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  4. ; ; ; ; (, IEEE BITS the Information Theory Magazine)
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  5. ; ; ; ; (, Designs, Codes and Cryptography)
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  6. ; ; ; ; (, Designs, Codes and Cryptography)
    null (Ed.)
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