Réseau des périodes des courbes $$y^q = \prod\limits_{j = 0}^n {(z - a_j )^{\alpha _j } } $$ (q premier)

Bennama, H.; Carbonne, P.

doi:10.1007/bf02567451

Cited by 6 publications

(1 citation statement)

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“…Serre found that the Klein quartic over the finite field F 2 3 is such a curve in [22]. There are many researches on its properties and applications to coding theory, for example [4,10,12,15,19]. We remark that the Klein quartic has a defining equation…”

Section: Introductionmentioning

confidence: 98%

A quotient curve of the Fermat curve of degree twenty-three attaining the Serre bound

Kawakita

2005

Journal of Pure and Applied Algebra

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The curve in the title is a non-maximal curve of genus 11, which has a defining equation analogous to the Klein quartic's. We study its properties and show how to apply it to coding theory.In 1970s, Goppa discovered algebraic geometric codes in [9]. His theory gives us a guarantee on the existence of efficient codes, when we have curves with many rational points for a fixed genus and a fixed finite field. It creates strong interest on such curves; see [8,18]. By a curve we mean a smooth absolutely irreducible projective curve.For the number of rational points on a curve C of genus g over a finite field F q , the Hasse-Weil boundis well-known. A curve is said to be maximal over F q , if it attains this bound. After the appearance of algebraic geometric codes, in 1983 Serre sharpened this bound in [20],

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