On the rank of certain finite fields |
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Authors: | Mohammad A Shokrollahi |
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Affiliation: | (1) Institut für Informatik V, Universität Bonn, Römerstr. 164, 5300 Bonn 1, GERMANY |
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Abstract: | In the present paper we shall show that the rank of the finite field
regarded as an
-algebra has one of the two values 2n or 2n+1 ifn satisfies 1/2q+1<n<1/2(m(q)–2). Herem(q) denotes the maximum number of
-rational points of an algebraic curve of genus 2 over
. Using results of Davenport-Hasse, Honda and Rück we shall give lower bounds form(q) which are close to the Hasse-Weil bound
. For specialq we shall further show thatm(q) is equal to the Hasse-Weil bound. |
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Keywords: | Bilinear complexity hyperelliptic curves finite fields Subject classifications 14H05 14H40 68Q20 |
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