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• W1952282106 abstract "For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We classify completely the intersections of the Hermitian curve with lines and parabolas (in the $mathbb{F}_{q^2}$ affine plane). Starting from both results, we are able to obtain geometric characterizations for small-weight codewords for some families of Hermitian codes over any $mathbb{F}_{q^2}$. From the geometric characterization, we obtain explicit formulae. In particular, we determine the number of minimum-weight codewords for all Hermitian codes with $dleq q$ and all second-weight codewords for distance-$3,4$ codes." @default.
• W1952282106 created "2016-06-24" @default.
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• W1952282106 date "2012-08-08" @default.
• W1952282106 modified "2023-09-27" @default.
• W1952282106 title "On the Hermitian curve, its intersections with some conics and their applications to affine-variety codes and Hermitian codes" @default.
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