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• W2255354810 endingPage "101621" @default.
• W2255354810 startingPage "101621" @default.
• W2255354810 abstract "In this paper we consider the Hermitian codes defined as the dual codes of one-point evaluation codes on the Hermitian curve H over the finite field Fq2. We focus on those with distance d≥q2−q and give a geometric description of the support of their minimum-weight codewords. We consider the unique writing μq+λ(q+1) of the distance d with μ,λ non negative integers, and μ≤q, and consider all the curves X of the affine plane AFq22 of degree μ+λ defined by polynomials with xμyλ as leading monomial with respect to the DegRevLex term ordering (with y>x). We prove that a zero-dimensional subscheme Z of AFq22 is the support of a minimum-weight codeword of the Hermitian code with distance d if and only if it is made of d simple Fq2-points and there is a curve X such that Z coincides with the scheme theoretic intersection H∩X (namely, as a cycle, Z=H⋅X). Finally, exploiting this geometric characterization, we propose an algorithm to compute the number of minimum weight codewords and we present comparison tables between our algorithm and MAGMA command MinimumWords." @default.
• W2255354810 created "2016-06-24" @default.
• W2255354810 creator A5008132460 @default.
• W2255354810 creator A5081137589 @default.
• W2255354810 date "2020-02-01" @default.
• W2255354810 modified "2023-09-25" @default.
• W2255354810 title "Hermitian codes and complete intersections" @default.
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• W2255354810 doi "https://doi.org/10.1016/j.ffa.2019.101621" @default.
• W2255354810 hasPublicationYear "2020" @default.
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