On additive polynomials and certain maximal curves
نویسندگان
چکیده
منابع مشابه
A Note on Certain Maximal Curves
We characterize certain maximal curves over finite fields whose plane models are of Hurwitz type, namely xy +y +x = 0. We also consider maximal hyperelliptic curves of maximal genus. Finally, we discuss maximal curves of type y + y = x via Class Field Theory.
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where C(Fq) denotes the set of Fq-rational points of the curve C. Here we will be interested in maximal(resp. minimal) curves over Fq2 , that is, we will consider curves C attaining Hasse-Weil’s upper (resp. lower) bound: #C(Fq2) = q + 1 + 2gq (resp. q + 1− 2gq). Here we are interested to consider the hyperelliptic curve C given by the equation y = x + 1 over Fq2 . We are going to determine whe...
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Algebraic Geometric codes associated to a recently discovered class of maximal curves are investigated. As a result, some linear codes with better parameters with respect to the previously known ones are discovered, and 70 improvements on MinT’s tables [1] are obtained.
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In general, this bound is sharp. In fact if q is a square, there exist several curves that attain the above upper bound (see [4], [5], [14] and [23]). We say a curve is maximal (resp. minimal) if it attains the above upper (resp. lower) bound. There are however situations in which the bound can be improved. For instance, if q is not a square there is a non-trivial improvement due to Serre (see ...
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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.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2008
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2008.03.008