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  1. Article: Orbit Structure of Grassmannian G2,m and a Decoder for Grassmann Code C(2, m).

    Piñero, Fernando L / Singh, Prasant

    IEEE transactions on information theory

    2022  Volume 69, Issue 3, Page(s) 1509–1520

    Abstract: In this article, we consider decoding Grassmann codes, linear codes associated to the Grassmannian and its embedding in a projective space. We look at the orbit structure of Grassmannian arising from the multiplicative ... ...

    Abstract In this article, we consider decoding Grassmann codes, linear codes associated to the Grassmannian and its embedding in a projective space. We look at the orbit structure of Grassmannian arising from the multiplicative group
    Language English
    Publishing date 2022-10-10
    Publishing country United States
    Document type Journal Article
    ISSN 0018-9448
    ISSN 0018-9448
    DOI 10.1109/TIT.2022.3213568
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Book ; Online: Codes with locality from cyclic extensions of Deligne-Lusztig curves

    Matthews, Gretchen L. / Piñero, Fernando L.

    2020  

    Abstract: Recently, Skabelund defined new maximal curves which are cyclic extensions of the Suzuki and Ree curves. Previously, the now well-known GK curves were found as cyclic extensions of the Hermitian curve. In this paper, we consider locally recoverable codes ...

    Abstract Recently, Skabelund defined new maximal curves which are cyclic extensions of the Suzuki and Ree curves. Previously, the now well-known GK curves were found as cyclic extensions of the Hermitian curve. In this paper, we consider locally recoverable codes constructed from these new curves, complementing that done for the GK curve. Locally recoverable codes allow for the recovery of a single symbol by accessing only a few others which form what is known as a recovery set. If every symbol has at least two disjoint recovery sets, the code is said to have availability. Three constructions are described, as each best fits a particular situation. The first employs the original construction of locally recoverable codes from curves by Tamo and Barg. The second yields codes with availability by appealing to the use of fiber products as described by Haymaker, Malmskog, and Matthews, while the third accomplishes availability by taking products of codes themselves. We see that cyclic extensions of the Deligne-Lusztig curves provide codes with smaller locality than those typically found in the literature.
    Keywords Computer Science - Information Theory ; Mathematics - Algebraic Geometry
    Subject code 516
    Publishing date 2020-06-11
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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