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We give a formula for the number of rational points of projective algebraic curves deened over a nite eld, and a bound \\ a l a W eil" for connected ones. More precisely, we give the characteristic polynomials of the Frobenius endomorphism on the etalè-adic cohomology groups of the curve. Finally, as an analogue of Artin's holomorphy conjecture, we p r o ve… (More)

Let q he a power of a prime number, Fq the finite field with q elements, n an integer dividing q-1, n > 2, and g a character of order n of the multiplicative group Fq. If X is an algebraic curve defined over Fq and if G is a divisor on X, we define a non linear code F(q, X, G, n, X) on an alphabet with n + 1 letters.We compute the parameters of this code,… (More)

- Yves Aubry, Marc Perret
- 2003

As an analogous of a conjecture of Artin, we show that, if Y −→ X is a finite flat morphism between two singular reduced absolutely irreducible projective algebraic curves defined over a finite field, then the numerator polynomial of the zeta function of X divides those of Y in Z[T]. We give some interpretations of this result in terms of semi-abelian… (More)

The aim of this paper is to explain how, starting from a Goppa Dχ is a non-principal degree 0 divisor on X associated to a character χ of Gal(Y /X), in the hope that X (G + Dχ) > X (G). We give, using a MAGMA program, several examples where this occurs, and where both the initial and twisted codes have same minimum distance, so that initial codes have been… (More)

- Marc Perret
- AAECC
- 1991

Let q be a power of an odd prime number and Fq be the finite field with q elements. We will construct a binary spherical code from an algebraic curve C defined over Fq and a rational divisor G on C, as the twist by the quadratic character 11 of the Goppa code L(G). The computation of the parameters of this code is based on the study of some character sums.… (More)

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