جستجوی مقالات مرتبط با کلیدواژه « maximal curves » در نشریات گروه « علوم پایه »
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The a-number is an invariant of the isomorphism class of the p-torsion group scheme. In this paper, we compute a closed formula for the a-number of yq + y =x(q+1)/3 and $sum_{t=1}^{s} y^{q⁄ 3^t}= xq+1$ with q = 3s over the finite field Fq2 using the action of the Cartier operator on H0(C,Ω1).Keywords: a-number, Cartier operator, Super-singular Curves, Maximal Curves}
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We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of minimum distance in several cases and get many records that don’t exist in MinT tables (tables of optimal parameters for linear codes), such as codes over F72 of dimension less than 36. Moreover, using maximal Hermitian curves and their sub-covers, we obtain a necessary and sufficient condition for self-orthogonality and Hermitian self-orthogonally of CL(D, G).
Keywords: Algebraic geometric codes, Maximal curves, Minimum distance, Goppa bound, Quantum error-correcting codes} -
In this paper, we compute a formula for the $a$-number of certain maximal curves given by the equation $y^{q}+y=x^{frac{q+1}{2}}$ over the finite field $mathbb{F}_{q^2}$. The same problem is studied for the maximal curve corresponding to $sum_{t=1}^s y^{q/2^t}=x^{q+1}$ with $q=2^s$, over the finite field $mathbb{F}_{q^2}$.
Keywords: $a$-number, Cartier operator, Super-singular Curves, Maximal Curves} -
In this note we review a simple criterion, due to Ekedahl, for superspecial curves defined over finite fields.Using this we generalize and give some simple proofs for some well-known superspecial curves.Keywords: Cartier operator, Supersingular curves, finite fields, maximal curves}
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