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    Optimum Linear Codes With Support-Constrained Generator Matrices Over Small Fields

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    Type
    Article
    Authors
    Yildiz, Hikmet cc
    Hassibi, Babak
    Date
    2019-12
    Permanent link to this record
    http://hdl.handle.net/10754/668615
    
    Metadata
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    Abstract
    We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a Reed-Solomon code of small field size and with the same minimum distance. In particular, if the code has length n , and maximum minimum distance d (over all generator matrices with the given support), then an optimal code exists for any field size q≥ 2n-d. As a by-product of this result, we settle the GM-MDS conjecture in the affirmative.
    Citation
    Yildiz, H., & Hassibi, B. (2019). Optimum Linear Codes With Support-Constrained Generator Matrices Over Small Fields. IEEE Transactions on Information Theory, 65(12), 7868–7875. doi:10.1109/tit.2019.2932663
    Sponsors
    This work was supported in part by the National Science Foundation under Grant CNS-0932428, Grant CCF-1018927, Grant CCF1423663, and Grant CCF-1409204, in part by Qualcomm Inc., in part by the NASAs Jet Propulsion Laboratory through the President and Directors Fund, and in part by the King Abdullah University of Science and Technology
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Information Theory
    DOI
    10.1109/tit.2019.2932663
    Additional Links
    https://ieeexplore.ieee.org/document/8786158/
    ae974a485f413a2113503eed53cd6c53
    10.1109/tit.2019.2932663
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