On the Hermitian curve and its intersections with some conics

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• 作者：Chiara Marcolla^a ; ^{chiara.marcolla@unitn.it" class="auth_mail} ; Marco Pellegrini^b ; ^{pellegrin@math.unifi.it" class="auth_mail} ; Massimiliano Sala^a ; ^{maxsalacodes@gmail.com" class="auth_mail}
• 关键词：11G20 ; 11T71
• 刊名：Finite Fields and Their Applications
• 出版年：July, 2014
• 年：2014
• 卷：28
• 期：Complete
• 页码：166-187
• 全文大小：355 K

文摘

We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In particular, we provide explicit counting formulas that have also applications to some Hermitian codes.