AbstractFor generalized Reed–Muller, GRM(q,d,n), codes, the determination of the second weight is still generally unsolved, it is an open question of Cherdieu and Rolland [J.P. Cherdieu, R. Rolland, On the number of points of some hypersurfaces in Fqn, Finite Fields Appl. 2 (1996) 214–224]. In order to answer this question, we study some maximal hypersurfaces and we compute the second weight of GRM(q,d,n) codes with the restriction that q⩾2d
AbstractWe study the functional codes Ch(X) defined by Lachaud in [G. Lachaud, Number of points of p...
In this work, we study the maximum number of F_q-rational points on a hypersurface of P^n . Given t...
Let GF(q) be the finite field with q elements of characteristic p, GF(q^m) be the extension of degre...
AbstractFor generalized Reed–Muller codes, whenqis large enough, we give the second codeword weight,...
AbstractThe weight distribution of the generalized Reed–Muller codes over the finite field Fq is lin...
AbstractWe study first some arrangements of hyperplanes in the n-dimensional projective space Pn(Fq)...
AbstractLet Fq be the finite field with q elements of characteristic p, Fqm be the extension of degr...
We give a complete conjectural formula for the number er(d, m) of maximum possible Fq-rational point...
International audienceWe consider the question of determining the maximum number of Fq-rational poin...
AbstractWe show that the minimum r-weight dr of an anticode can be expressed in terms of the maximum...
In J.-P. Serre's Lettre et M. Tsfasman [3], an interesting bound for the maximal number of points on...
AbstractWe show explicit estimates on the number of q-ratinoal points of an Fq-definable affine abso...
International audienceThe second weight of the Generalized Reed-Muller code of length q n and order ...
We present bounds on the number of points in algebraic curves and algebraic hypersurfaces in P-n(F-q...
AbstractIn this paper we prove that a set of points (in a projective space over a finite field of q ...
AbstractWe study the functional codes Ch(X) defined by Lachaud in [G. Lachaud, Number of points of p...
In this work, we study the maximum number of F_q-rational points on a hypersurface of P^n . Given t...
Let GF(q) be the finite field with q elements of characteristic p, GF(q^m) be the extension of degre...
AbstractFor generalized Reed–Muller codes, whenqis large enough, we give the second codeword weight,...
AbstractThe weight distribution of the generalized Reed–Muller codes over the finite field Fq is lin...
AbstractWe study first some arrangements of hyperplanes in the n-dimensional projective space Pn(Fq)...
AbstractLet Fq be the finite field with q elements of characteristic p, Fqm be the extension of degr...
We give a complete conjectural formula for the number er(d, m) of maximum possible Fq-rational point...
International audienceWe consider the question of determining the maximum number of Fq-rational poin...
AbstractWe show that the minimum r-weight dr of an anticode can be expressed in terms of the maximum...
In J.-P. Serre's Lettre et M. Tsfasman [3], an interesting bound for the maximal number of points on...
AbstractWe show explicit estimates on the number of q-ratinoal points of an Fq-definable affine abso...
International audienceThe second weight of the Generalized Reed-Muller code of length q n and order ...
We present bounds on the number of points in algebraic curves and algebraic hypersurfaces in P-n(F-q...
AbstractIn this paper we prove that a set of points (in a projective space over a finite field of q ...
AbstractWe study the functional codes Ch(X) defined by Lachaud in [G. Lachaud, Number of points of p...
In this work, we study the maximum number of F_q-rational points on a hypersurface of P^n . Given t...
Let GF(q) be the finite field with q elements of characteristic p, GF(q^m) be the extension of degre...
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