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- W2057886417 abstract "We determine conditions on $q$ for the nonexistence of deep holes ofthe standard Reed-Solomon code of dimension $k$ over $mathbb F_q$generated by polynomials of degree $k+d$. Our conditions rely on theexistence of $q$-rational points with nonzero, pairwise-distinctcoordinates of a certain family of hypersurfaces defined over $mathbb F_q$.We show that the hypersurfaces under consideration are invariantunder the action of the symmetric group of permutations of thecoordinates. This allows us to obtain critical informationconcerning the singular locus of these hypersurfaces, from which theexistence of $q$-rational points is established." @default.
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- W2057886417 date "2012-01-01" @default.
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- W2057886417 title "Singularities of symmetric hypersurfaces and Reed-Solomon codes" @default.
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- W2057886417 doi "https://doi.org/10.3934/amc.2012.6.69" @default.
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