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

Número: 
5
Ano: 
2014
Autor: 
Saeed Tafazolian
Arnoldo Teheran-Herrera
Fernando Torres
Abstract: 

We construct examples of curves defined over the finite field Fq6 which are covered by the GK-curve. Thus such curves are maximal over Fq6 although they cannot be covered by the Hermitian curve for q > 2. We also give examples of maximal curvesthat cannot be Galois covered by the Hermitian curve over the finite field Fq2n with n > 3 odd and q > 2. We point out some applications to codes related to an array coming from telescopic semigroups.

Keywords: 
finite field
maximal curve
Hermitian curve
GK-curve
generalized GK-curve
Mathematics Subject Classification 2010 (MSC 2010): 
11G20; 11M38; 14G15; 14H25
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