Further examples of maximal curves which cannot be covered by the Hermitian curve

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• 作者：Saeed Tafazolian^a ; ^{tafazolian@aut.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Arnoldo Teherá ; n-Herrera^b ; ¹ ; ^{ateheran@uis.edu.co" class="auth_mail" title="E-mail the corresponding author} ; Fernando Torres^c ; ^{ftorres@ime.unicamp.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11G20 ; 11M38 ; 14G15 ; 14H25
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：220
• 期：3
• 页码：1122-1132
• 全文大小：352 K

文摘

We construct examples of curves defined over the finite field urce">F_q⁶${\mathbb{F}}_{q^6}$ which are covered by the GK-curve. Thus such curves are maximal over urce">F_q⁶${\mathbb{F}}_{q^6}$ although they cannot be covered by the Hermitian curve for urce">q>2$q>2$. We also give examples of maximal curves that cannot be Galois covered by the Hermitian curve over the finite field urce">F_q²ⁿ${\mathbb{F}}_{q^{2n}}$ with urce">n>3$n>3$ odd and urce">q>2$q>2$. We point out some applications to codes related to an array coming from telescopic semigroups.