Constructing Partial MDS Codes from Reducible Curves
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining idea...
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Zusammenfassung: | We propose reducible algebraic curves as a mechanism to construct Partial MDS
(PMDS) codes geometrically. We obtain new general existence results, new
explicit constructions and improved estimates on the smallest field sizes over
which such codes can exist. Our results are obtained by combining ideas from
projective algebraic geometry, combinatorics and probability theory. |
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DOI: | 10.48550/arxiv.2007.14829 |