Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
We recall the construction of the Reed-Muller hermitian codes and some results about hermitians forms and exponential sums. With the help of these results, we give the weight distribution of the Reed-Muller hermitian codes and give some examples for which experimental computations have been made.
ISSN: 0938-1279

hal-00771918
https://hal.univ-antilles.fr/hal-00771918

Éditeur(s) : HAL CCSD
Résumé : 3rd cycle
https://cel.archives-ouvertes.fr/cel-00374738

Droits : info:eu-repo/semantics/OpenAccess
cel-00374738
https://cel.archives-ouvertes.fr/cel-00374738
https://cel.archives-ouvertes.fr/cel-00374738/document
https://cel.archives-ouvertes.fr/cel-00374738/file/Cherdieu2000.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We build a class of codes using hermitian forms and the functional trace code. Then we give a general expression of the r-th minimum distance of our code and compute general bounds for the weight hierarchy by using exponential sums. We also get the minimum distance and calculate the r-th generalized Hamming weight dr in some special cases.
ISSN: 1071-5797

hal-00771922
https://hal.univ-antilles.fr/hal-00771922

Éditeur(s) : HAL CCSD
Résumé : 17 pages
We look at the number of solutions of an equation of the form f_1*f_2*...*f_k=a in a finite field, where each f_i is a multilinear polynomial. We use two methods to construct a solution of this problem for the cases a=0, a<>0, and we generally get a semi-explicit formula. We show that this formula can generate a more efficient algorithm than the traditional algorithm which consists to make a systematic computation. We also give explicit formulas in some special cases, and an application of our main result to the search of the weight hierarchy of the multilinear code with separated variables.
https://hal.univ-antilles.fr/hal-00772478

hal-00772478
https://hal.univ-antilles.fr/hal-00772478
ARXIV : math.NT/0603057

Éditeur(s) : HAL CCSD
Résumé : International audience
Actes du colloque Carribean Mathematical Colloquium
Pointe-à-Pitre, Guadeloupe

hal-00771907
https://hal.univ-antilles.fr/hal-00771907